C₂₃×#1512 #15669131

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1512

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

222 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 736

A minimal faithful permutation representation — 3 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)(25,29)(26,27)(30,31)(32,33)(34,40,42,37)(35,38)(36,39)(41,46,47,44)(43,45);(24,25)(26,29)(27,31)(28,30)(32,34)(33,37)(35,41)(36,42)(38,44)(39,40)(43,47)(45,46);(24,26,28,27)(25,29,30,31)(32,35,36,43)(33,38,39,45)(34,41,42,47)(37,44,40,46)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8497, C₂₃×#8498, C₂₃×#8499, …
maximal normal subgroup of	C₂₃×#8497, C₂₃×#8498, C₂₃×#8499, …
maximal quotient of	C₂₃×#7594, C₂₃×#7596, C₂₃×#7601, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 244);