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C3×D4865 #44415902

order29190
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4865
unambiguous semidirect productC5⋊(C3×D973)

Splittings

Fitting, socle, HallC3×C5×C7×C139 ⋊ C2
derived, HallC5×C7×C139 ⋊ C2×C3
HallC3×C7×C139 ⋊ D5
HallC3×C5×C139 ⋊ D7
HallC7×C139 ⋊ C3×D5
HallC5×C139 ⋊ C3×D7
HallC3×C139 ⋊ D35
SylowC139 ⋊ C3×D35
HallC3×C5×C7 ⋊ D139
HallC5×C7 ⋊ C3×D139
HallC3×C7 ⋊ D695
HallC3×C5 ⋊ D973
SylowC7 ⋊ C3×D695
SylowC5 ⋊ C3×D973

Subgroups

subgroupG/H
center, hypercenterC3D4865
commutator, cosocle, hypocenterC5×C7×C139C2×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C139C2
LCSG ▷ C5×C7×C139
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 154
transitive degreeμt(G) = 14595

A minimal faithful permutation representation — 2 generators on 154 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154);(5,8)(6,7)(10,15)(11,14)(12,13)(17,154)(18,153)(19,152)(20,151)(21,150)(22,149)(23,148)(24,147)(25,146)(26,145)(27,144)(28,143)(29,142)(30,141)(31,140)(32,139)(33,138)(34,137)(35,136)(36,135)(37,134)(38,133)(39,132)(40,131)(41,130)(42,129)(43,128)(44,127)(45,126)(46,125)(47,124)(48,123)(49,122)(50,121)(51,120)(52,119)(53,118)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)

Conjugacy classes & character table

7302 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29190, 12);