C₂₃×#2983 #15670602

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2983

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂³×C₂₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

356 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 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)(24,25,26,29,27,28,30,31)(32,33)(34,40)(35,38)(36,39)(37,42)(41,46)(43,45)(44,47);(32,34,36,42)(33,37,39,40)(35,43,44,41)(38,46,47,45);(25,28)(29,31)(32,35,36,44)(33,38,39,47)(34,41,42,43)(37,45,40,46);(33,39)(37,40)(38,47)(45,46)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8838, C₂₃×#8865, C₂₃×#8962, …
maximal normal subgroup of	C₂₃×#8838, C₂₃×#8865, C₂₃×#8962, …
maximal quotient of	C₂₃×#20534, C₂₃×#20536, C₂₃×#20570, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1715);