C₂₃×#2133 #15669752

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2133

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×#99
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×Q₈	C₂³×C₂₃
prime radical	C₂×#41×C₂₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂³×C₂₃ ◁ C₂²×Q₈×C₂₃ ◁ G

230 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 84 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)(24,25,28,32,29,33,44,51)(26,34,37,52,35,48,42,54)(27,38,40,50,41,31,43,49)(30,45,47,39,46,53,55,36);(24,26)(25,30)(27,39)(28,42)(29,35)(31,48)(32,47)(33,46)(34,38)(36,41)(37,44)(40,45)(43,53)(49,54)(50,52)(51,55);(26,35)(30,46)(34,48)(36,39)(37,42)(45,53)(47,55)(52,54)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12709, C₂₃×#12710, C₂₃×#12729, …
maximal normal subgroup of	C₂₃×#12709, C₂₃×#12710, C₂₃×#12729, …
maximal quotient of	C₂₃×#11432, C₂₃×#11448, C₂₃×#11480, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 865);