C₂₃×#1699 #15669318

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#1699

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂×D₄×C₂₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1699, C₂₃×#19142, C₂₃×#19156, …
maximal normal subgroup of	C₂×C₂₃×#1699, C₂₃×#19142, C₂₃×#19156, …
maximal quotient of	C₂₃×#8654, C₂₃×#9225, C₂₃×#9227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 431);