Dic₃×#14274263 #37524797

order	22932
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×#14274263
unambiguous semidirect product	C₃⋊(C₄×#14274263)

Splittings

derived	C₃×C₇²×C₁₃ ⋊ C₃×C₄
Hall	C₃×#14274263 ⋊ C₄
Hall	C₇²×C₁₃ ⋊ C₃×Dic₃
Sylow	C₇² ⋊ Dic₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ Dic₃×#3861

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#14274263
commutator, hypocenter	C₃×C₇²×C₁₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₃×#14274263	C₂
LCS	G ▷ C₃×C₇²×C₁₃
UCS	C₁ ◁ C₂

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 7644

A minimal faithful permutation representation — 3 generators on 34 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(15,16)(17,18,19,20)(22,23,24)(25,27,26)(29,30,31)(32,34,33);(1,2,4,3,6,10,7,11,13,5,8,12,9)(14,15,16)(28,29,30,32,31,33,34);(21,22,23,25,24,26,27)

Conjugacy classes & character table

1290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 742);

Dic3×#14274263 #37524797