C₂×C₂₃×#64425 #27214166

order	13524
isoclinism	isoclinic class of #64425
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₃ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product

C₂×C₂₃×#64425

Splittings

Fitting, socle	C₂×C₇²×C₂₃ ⋊ C₂×C₃
derived, Sylow	C₇² ⋊ C₂²×C₃×C₂₃
Hall	C₂×C₂₃×C₇⋊D₇ ⋊ C₃
Hall	C₂₃×#3862 ⋊ C₂²
Hall	C₇²×C₂₃ ⋊ C₂²×C₃
Hall	C₂×C₇⋊D₇ ⋊ C₃×C₂₃
Hall	#3862 ⋊ C₂²×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₃	#64425
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₂₃	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₂₃

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 966

A minimal faithful permutation representation — 2 generators on 39 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13524, 100);

C2×C23×#64425 #27214166