C₂₃×#1657 #15669276

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1657

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂₃×#496	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

206 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 60 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 — 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)(25,28)(26,30)(29,31)(33,38)(34,41)(35,36)(40,43)(42,44)(45,46);(26,30)(28,31)(32,33)(34,39)(35,43)(36,38)(37,40)(41,46)(42,47)(44,45);(24,25)(26,31)(27,29)(28,30)(32,34,37,42)(33,39,40,47)(35,41,36,44)(38,45,43,46)

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13679, C₂×C₂₃×#1657, C₂₃×#18984, …
maximal normal subgroup of	C₂₃×#13679, C₂×C₂₃×#1657, C₂₃×#18984, …
maximal quotient of	C₂₃×#7736, C₂₃×#7738, C₂₃×#7740, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 389);