C₂₃×#1813 #15669432

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1813

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#117
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#380
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂×M₁₆×C₂₃ ◁ G

252 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 116 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)(24,25,29,33,30,34,28,43)(26,35,38,46,39,50,37,31)(27,40,41,47,42,32,44,48)(36,51,52,55,53,49,54,45);(24,26,28,37,30,39,29,38)(25,31,33,35,34,46,43,50)(27,36,41,52,42,53,44,54)(32,45,47,49,40,55,48,51);(24,27)(25,32)(26,36)(28,41)(29,44)(30,42)(31,45)(33,47)(34,40)(35,49)(37,52)(38,54)(39,53)(43,48)(46,55)(50,51)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7227, C₂₃×#7229, C₂₃×#11870, …
maximal normal subgroup of	C₂₃×#7227, C₂₃×#7229, C₂₃×#11870, …
maximal quotient of	C₂₃×#8601, C₂₃×#8602, C₂₃×#8603, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 545);