C₂₃×#1812 #15669431

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

Aliases

direct product

C₂₃×#1812

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

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

normal subgroups only

This group has 260 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)(26,34)(27,38,40,31)(28,41)(29,33)(30,36)(32,42)(35,48,50,46)(37,47)(39,45,54,53)(43,49,52,55)(44,51);(24,26,28,36,29,37,42,51)(25,30,32,34,33,44,41,47)(27,35,39,49,40,50,54,55)(31,43,45,46,38,52,53,48);(24,27)(25,31)(26,35)(28,39)(29,40)(30,43)(32,45)(33,38)(34,46)(36,49)(37,50)(41,53)(42,54)(44,52)(47,48)(51,55)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7227, C₂₃×#7228, C₂₃×#11867, …
maximal normal subgroup of	C₂₃×#7227, C₂₃×#7228, C₂₃×#11867, …
maximal quotient of	C₂₃×#8601, C₂₃×#8602, C₂₃×#8603, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 544);