C₂₃×#1554 #15669173

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1554

Subgroups

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

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

normal subgroups only

This group has 198 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) = 55
transitive degree	μ_t(G) = 1472

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8490, C₂₃×#8501, C₂₃×#8503, …
maximal normal subgroup of	C₂₃×#8490, C₂₃×#8501, C₂₃×#8503, …
maximal quotient of	C₂₃×#7581, C₂₃×#7583, C₂₃×#7611, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 286);