C₂₃×#1833 #15669452

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1833

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#117
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#382
prime radical	C₂³×C₂₃	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂₃×#117 ◁ G

172 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 100 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)(26,34,37,30)(27,38,40,53)(28,33)(29,32)(31,39,44,54)(35,48)(36,47,51,43)(41,45)(42,49)(46,55)(50,52);(24,26,28,36,29,37,41,51)(25,30,33,43,32,34,45,47)(27,35,39,49,40,50,54,55)(31,42,38,52,44,46,53,48);(24,27)(25,31,32,44)(26,35)(28,39)(29,40)(30,42,34,46)(33,38,45,53)(36,49)(37,50)(41,54)(43,52,47,48)(51,55)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12826, C₂₃×#12827, C₂₃×#12828, …
maximal normal subgroup of	C₂₃×#12826, C₂₃×#12827, C₂₃×#12828, …
maximal quotient of	C₂₃×#8780, C₂₃×#8781, C₂₃×#8782, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 565);