C₂₃×#2220 #15669839

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2220

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂₃×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

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

normal subgroups only

This group has 160 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) = 43
transitive degree	μ_t(G) = 1472

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2220, C₂₃×#33604, C₂₃×#33605, …
maximal normal subgroup of	C₂×C₂₃×#2220, C₂₃×#33604, C₂₃×#33605, …
maximal quotient of	C₂₃×#12435, C₂₃×#12444, C₂₃×#12456, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 952);