Finite Group Databasebeta

D3×C199 #11924758

order1194
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C199 · Schur multiplier (H2) = C1

Aliases

direct productD3×C199
unambiguous semidirect productC3⋊(C2×C199)

Splittings

Fitting, socle, HallC3×C199 ⋊ C2
derived, SylowC3 ⋊ C2×C199

Subgroups

subgroupG/H
center, hypercenterC199D3
commutator, cosocle, hypocenterC3C2×C199
FrattiniC1G
Fitting, socleC3×C199C2
LCSG ▷ C3
UCSC1 ◁ C199

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 202
transitive degreeμt(G) = 597

A minimal faithful permutation representation — 2 generators on 202 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202);(2,3)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×D199, C2×D3×C199, D9×C199, …
maximal normal subgroup ofD3×D199, C2×D3×C199, D3×C199⋊C3, …
maximal quotient ofDic3×C199, C2×D3×C199, D9×C199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1194, 3);