C₂₃×#2239 #15669858

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2238
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#2239

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#481
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂³×C₂₃	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×M₁₆×C₂₃ ◁ G

124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 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)(26,34,35,52)(27,38,39,55)(28,43,41,32)(30,45,46,36)(31,48,49,42)(37,50,44,53)(40,47,54,51);(27,39)(31,49)(34,52)(36,45)(38,55)(40,54)(42,48)(50,53);(24,26,28,44,29,35,41,37)(25,30,32,51,33,46,43,47)(27,40,42,45,39,54,48,36)(31,50,38,52,49,53,55,34)

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12299, C₂₃×#12300, C₂₃×#12302, …
maximal normal subgroup of	C₂₃×#12299, C₂₃×#12300, C₂₃×#12302, …
maximal quotient of	C₂₃×#12875, C₂₃×#12931, C₂₃×#13009, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 971);