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C2×C3×C3⋊(D191⋊C5) #46806012

order34380
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C3⋊(D191⋊C5)
unambiguous semidirect product(C2×C3)⋊(C3×D191⋊C5)
unambiguous semidirect product(C2×C191⋊C5)⋊(C3×D3)
unambiguous semidirect product(C2×D573)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D573)⋊C5

Splittings

Fitting, socleC2×C32×C191 ⋊ C2×C5
derivedC3×C191 ⋊ C22×C3×C5
HallC32×C191⋊C5 ⋊ C22
HallC2×C3×D573 ⋊ C5
HallC32×C191 ⋊ C22×C5
HallC191⋊C5 ⋊ C2×C3×D3
SylowC191 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×D191⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D191⋊C5)
commutator, cosocle, hypocenterC3×C191C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C191C2×C5
LCSG ▷ C3×C191
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 199
transitive degreeμt(G) = 2292

A minimal faithful permutation representation — 2 generators on 199 points:

(3,4,5)(7,8)(10,14,15,33,38,11,12,20,22,62)(13,27,28,88,93,17,18,49,51,142)(16,43,44,45,73,24,25,79,81,83)(19,56,57,160,162,30,31,102,103,133)(21,67,68,175,125,35,36,120,122,111)(23,77,48,74,75,40,41,78,39,82)(26,85,86,92,150,46,47,140,123,149)(29,98,99,163,131,53,54,104,146,180)(32,108,109,151,61,59,60,94,148,42)(34,115,116,63,119,64,65,171,112,113)(37,126,127,161,186,70,71,174,178,187)(50,147,110,139,69,90,91,84,169,124)(52,153,154,55,132,95,96,191,76,101)(58,165,166,192,181,105,106,197,159,190)(66,135,136,143,158,118,80,183,100,188)(72,155,177,138,121,129,130,193,179,176)(87,168,172,173,134,107,141,117,189,182)(89,97,128,114,185,144,145,156,170,152)(137,194,167,196,198,184,157,164,195,199);(1,2)(6,7,8)(9,10,13,19,32,61,40,20,34,66,119,169,145,95,49,89,146,189,106,167,99,102,161,196,194,54,100,51,94,152,184,135,25,45,84,108,129,70,35,12,16,26,48,77,133,176,36,69,125,38,73,131,181,91,148,160,171,168,198,158,122,177,197,183,101,159,96,155,127,172,115,47,87,105,56,68,123,90,18,29,55,74,33,63,114,71,128,179,75,79,134,154,149,142,187,86,140,186,93,150,191,182,44,82,138,156,126,170,112,22,39,76,53,27,50,92,120,31,58,107,85,65,117,174,130,153,192,132,136,166,193,175,188,199,141,116,103,151,147,190,180,83,62,111,124,67,121,162,41,78,46,24,14,21,37,72,60,110,81,43,80,137,185,109,88,143,98,157,195,178,57,104,164,165,173,163,144,28,52,97,139,113,118,64,15,23,42,59,30,17,11)

Conjugacy classes & character table

432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34380, 67);