C₂₃×#1422 #15669041

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₃×#1422

Subgroups

	subgroup	G/H
center	C₁₆×C₂₃	D₄
commutator	C₄	C₂×C₁₆×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
socle	C₂×C₂₃	C₄⋊C₁₆
prime radical	C₂²×C₂₃	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,34,29,35,43,50,30,33,44,48,40,49,53,55,31,36,45,51,38,32,46,47,27,41,42,54,26,37,39,52);(24,26,27,38,31,40,30,29)(25,32,33,37,36,35,41,49)(28,39,42,46,45,53,44,43)(34,47,48,52,51,50,54,55)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7381, C₂₃×#7382, C₂₃×#7447, …
maximal normal subgroup of	C₂₃×#7381, C₂₃×#7382, C₂₃×#7447, …
maximal quotient of	C₂₃×#7455, C₂₃×#7458, C₂₃×#7467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 154);

C23×#1422 #15669041