C₂₃×#1376 #15668995

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1376

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₃	D₄
commutator	C₄	C₄×C₈×C₂₃
Frattini, cosocle	C₂²×C₈	C₂²×C₂₃
socle	C₂²×C₂₃	C₄⋊C₈
prime radical	C₂³×C₂₃	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 2 generators on 43 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)(28,29,31,36,32,35,39,42,33,37,40,43,30,34,38,41);(25,27)(29,34,37,35)(36,41,43,42)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7107, C₂₃×#7108, C₂₃×#7114, …
maximal normal subgroup of	C₂₃×#7107, C₂₃×#7108, C₂₃×#7114, …
maximal quotient of	C₂₃×#7138, C₂₃×#7143, C₂₃×#7146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 108);

C23×#1376 #15668995