C₂₃×#2028 #15669647

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

Aliases

direct product

C₂₃×#2028

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂³×C₂₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

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

normal subgroups only

This group has 246 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) = 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)(24,25,27,29)(26,30,31,28)(32,33)(34,40)(35,43)(36,39)(37,41)(38,44)(42,47)(45,46);(24,26,27,31)(25,28,29,30)(35,44)(37,46)(38,43)(41,45);(32,34,36,42)(33,37,39,46)(35,45,44,41)(38,47,43,40)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7431, C₂₃×#12210, C₂₃×#12212, …
maximal normal subgroup of	C₂₃×#7431, C₂₃×#12210, C₂₃×#12212, …
maximal quotient of	C₂₃×#10341, C₂₃×#10342, C₂₃×#10345, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 760);