C₂×C₂₃×#391 #15669913

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×C₂₃×#391

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₃	C₂³
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 4 generators on 41 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₃×#1272, C₂₃×#7575, C₂₃×#7595, …
maximal normal subgroup of	C₂×C₂₃×#1272, C₂₃×#7575, C₂₃×#7595, …
maximal quotient of	C₂×C₂₃×C₄⋊#95, C₂×C₂₃×#1436, C₄×C₂₃×#391, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1026);

C2×C23×#391 #15669913