C₂₃×#1680 #15669299

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#1680

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

150 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 2944

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

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1680, C₂₃×#19123, C₂₃×#19124, …
maximal normal subgroup of	C₂×C₂₃×#1680, C₂₃×#19123, C₂₃×#19124, …
maximal quotient of	C₂₃×#8647, C₂₃×#9218, C₂₃×#9220, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 412);