C₂₃×#1637 #15669256

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1637

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂×D₄×C₂₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1637, C₂₃×#18494, C₂₃×#18517, …
maximal normal subgroup of	C₂×C₂₃×#1637, C₂₃×#18494, C₂₃×#18517, …
maximal quotient of	C₂₃×#7764, C₂₃×#7766, C₂₃×#7772, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 369);