C₂₃×#1436 #15669055

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#1436

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₃	C₂³
commutator	C₂²	C₂×C₄²×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

612 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2944

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)(25,27)(28,29,31,30)(33,35)(36,37,39,38);(32,33)(34,35)(36,37,39,38);(24,25)(26,27)(28,30,31,29)(32,33)(34,35)(36,38,39,37)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7215, C₂₃×#8347, C₂×C₂₃×#1436, …
maximal normal subgroup of	C₂₃×#7215, C₂₃×#8347, C₂×C₂₃×#1436, …
maximal quotient of	C₂₃×#7554, C₂₃×#7556, C₂₃×#7557, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 168);

C23×#1436 #15669055