C₂₃×#2053 #15669672

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2053

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#394
prime radical	C₂₃×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

264 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 80 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)(26,35)(27,40)(28,45)(29,33)(30,34)(31,37)(32,42)(36,46)(38,48)(39,47)(41,49)(43,50)(44,53)(51,54)(52,55);(24,26)(25,31)(27,41)(28,38)(29,37)(30,39)(32,49)(33,47)(34,48)(35,45)(36,43)(40,46)(42,52)(44,51)(50,54)(53,55);(24,27,28,42,30,44,29,43)(25,32,33,40,34,50,45,53)(26,36,37,51,39,52,38,41)(31,46,35,49,48,55,47,54)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12170, C₂₃×#12171, C₂₃×#12172, …
maximal normal subgroup of	C₂₃×#12170, C₂₃×#12171, C₂₃×#12172, …
maximal quotient of	C₂₃×#10464, C₂₃×#10465, C₂₃×#10466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 785);