C₂₃×#3028 #15670647

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3026
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#3028

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂₃×#585	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

716 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 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)(26,30,36,43)(27,31,38,45)(28,39,40,32)(34,46,48,41)(35,49,50,42)(37,51,52,44)(47,53,55,54);(24,26)(25,30)(27,34)(28,35)(29,36)(31,41)(32,42)(33,43)(37,47)(38,48)(39,49)(40,50)(44,53)(45,46)(51,54)(52,55);(24,27)(25,31)(26,34)(28,37)(29,38)(30,41)(32,44)(33,45)(35,47)(36,48)(39,51)(40,52)(42,53)(43,46)(49,54)(50,55);(24,28,29,40)(25,32,33,39)(26,35,36,50)(27,37,38,52)(30,42,43,49)(31,44,45,51)(34,47,48,55)(41,53,46,54)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13351, C₂₃×#13352, C₂₃×#13354, …
maximal normal subgroup of	C₂₃×#13351, C₂₃×#13352, C₂₃×#13354, …
maximal quotient of	C₂₃×#18308, C₂₃×#18309, C₂₃×#18310, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1760);