C₂₃×#2038 #15669657

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2038

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

278 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 736

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)(25,26)(28,29)(30,33)(31,34)(32,36)(35,40)(37,41)(38,43)(39,42);(24,25)(26,27)(28,30,32,38)(29,33,36,43)(31,39,40,37)(34,42,35,41);(24,26,27,25)(29,34)(31,40)(33,41)(35,36)(37,39)(42,43)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2038, C₂₃×#23492, C₂₃×#23494, …
maximal normal subgroup of	C₂×C₂₃×#2038, C₂₃×#23492, C₂₃×#23494, …
maximal quotient of	C₂₃×#10396, C₂₃×#10397, C₂₃×#10400, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 770);