C₂₃×#2054 #15669673

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2054

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂²×D₈×C₂₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 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)(26,27)(33,38)(34,39)(35,36);(28,29)(30,31)(32,33)(34,35)(36,38)(37,39);(25,27)(29,31)(32,34,35,33,37,38,36,39)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7080, C₂₃×#7088, C₂₃×#12158, …
maximal normal subgroup of	C₂₃×#7080, C₂₃×#7088, C₂₃×#12158, …
maximal quotient of	C₂₃×#10472, C₂₃×#10473, C₂₃×#10484, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 786);