C₂₃×#1367 #15668986

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

Aliases

direct product

C₂₃×#1367

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₃	D₄
commutator	C₄	C₂×C₁₆×C₂₃
Frattini, cosocle	C₄×C₈	C₂²×C₂₃
socle, prime radical	C₂²×C₂₃	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 2 generators on 47 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)(26,30)(29,31)(32,33,34,37,35,38,40,43,36,39,41,44,42,45,46,47);(24,25,26,28,27,29,30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7070, C₂₃×#7071, C₂₃×#7074, …
maximal normal subgroup of	C₂₃×#7070, C₂₃×#7071, C₂₃×#7074, …
maximal quotient of	C₂₃×#7099, C₂₃×#7151, C₂₃×#7455, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 99);

C23×#1367 #15668986