C₂₃×#3093 #15670712

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#3093

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 184 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 — 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)(34,37)(35,38)(36,39)(40,43)(41,44)(42,45)(46,47);(25,28)(29,31)(32,34,36,42)(33,37,39,45)(35,41,43,47)(38,44,40,46);(24,26,27,30)(25,29,28,31)(33,38)(35,43)(37,44)(39,40)(41,47)(45,46);(33,39)(37,45)(38,40)(44,46)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#24020, C₂₃×#24021, C₂₃×#24022, …
maximal normal subgroup of	C₂₃×#24020, C₂₃×#24021, C₂₃×#24022, …
maximal quotient of	C₂₃×#20701, C₂₃×#20845, C₂₃×#20910, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1825);