C₂₃×#1916 #15669535

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1916

Subgroups

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 3 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)(30,33)(31,32)(34,35)(36,37,41,38,40,43,39,42);(29,32)(33,35)(36,38,41,43,40,42,39,37);(25,27)(28,30,31,34)(29,33,32,35)(36,39,40,41)(37,42,43,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₃×#1916, C₂₃×#21020, C₂₃×#21022, …
maximal normal subgroup of	C₂×C₂₃×#1916, C₂₃×#21020, C₂₃×#21022, …
maximal quotient of	C₂₃×#9533, C₂₃×#9534, C₂₃×#9535, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 648);

C23×#1916 #15669535