C₂₃×#1612 #15669231

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1612

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#538	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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)(32,33,36,39)(34,37,41,44)(35,38,42,45)(40,46,47,43);(24,25)(26,29)(27,31)(28,30)(32,34)(33,37)(35,40)(36,41)(38,43)(39,44)(42,47)(45,46);(24,26,28,27)(25,29,30,31)(32,35,36,42)(33,38,39,45)(34,40,41,47)(37,43,44,46)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1612, C₂₃×#18121, C₂₃×#18126, …
maximal normal subgroup of	C₂×C₂₃×#1612, C₂₃×#18121, C₂₃×#18126, …
maximal quotient of	C₂₃×#7795, C₂₃×#7796, C₂₃×#7799, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 344);