C₂₃×#2097 #15669716

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2097

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

238 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 51
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(28,29,31,33)(30,34,35,32)(36,37,39,43,40,44,48,41)(38,45,46,50,47,51,49,42);(24,25)(26,27)(28,30,31,35)(29,32,33,34)(37,41)(39,48)(42,45)(43,44)(46,49)(50,51);(25,27)(36,38,40,47)(37,42,44,50)(39,49,48,46)(41,45,43,51)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2097, C₂₃×#23730, C₂₃×#23732, …
maximal normal subgroup of	C₂×C₂₃×#2097, C₂₃×#23730, C₂₃×#23732, …
maximal quotient of	C₂₃×#10664, C₂₃×#10669, C₂₃×#10675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 829);