C₂₃×#2074 #15669693

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2074

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

222 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 51
transitive degree	μ_t(G) = 2944

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7413, C₂×C₂₃×#2074, C₂₃×#23627, …
maximal normal subgroup of	C₂₃×#7413, C₂×C₂₃×#2074, C₂₃×#23627, …
maximal quotient of	C₂₃×#10623, C₂₃×#10624, C₂₃×#10626, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 806);