C₃×D₇²×C₂₃ #27214182

order	13524
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×D₇²×C₂₃

Splittings

Fitting, socle, Hall	C₃×C₇²×C₂₃ ⋊ C₂²
derived, Sylow	C₇² ⋊ C₂²×C₃×C₂₃
Hall	C₇²×C₂₃ ⋊ C₂²×C₃
Hall	C₃×C₇² ⋊ C₂²×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₇²
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₂₃	C₂²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₂₃

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 966

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,29,30,28,26)(32,33)(34,35)(36,37)(38,39,40);(25,26)(27,28)(29,30)(31,32,34,36,37,35,33)

Conjugacy classes & character table

1725 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13524, 116);

C3×D72×C23 #27214182