C₂₃×#2080 #15669699

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2080

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#397
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

190 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 55 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)(26,34,37,47)(27,31)(28,32)(29,33)(30,36,44,41)(35,50,38,49)(39,45)(40,46)(42,48)(43,52,54,51)(53,55);(24,26)(25,30)(27,38)(28,41)(29,37)(31,43)(32,47)(33,44)(34,48)(35,40)(36,42)(39,51)(45,50)(46,54)(49,55)(52,53);(24,27,28,39,29,40,42,53)(25,31,32,45,33,46,48,55)(26,35,36,51,37,38,41,52)(30,43,34,49,44,54,47,50)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2080, C₂₃×#23649, C₂₃×#23833, …
maximal normal subgroup of	C₂×C₂₃×#2080, C₂₃×#23649, C₂₃×#23833, …
maximal quotient of	C₂₃×#10627, C₂₃×#10628, C₂₃×#10629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 812);