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C₂×C₂₃×#343 #15669360

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₂₃×#343

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²⋊C₄
commutator	C₂²	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7251, C₄×C₂₃×#343, C₂₃×#10727, …
maximal normal subgroup of	C₂₃×#7251, C₄×C₂₃×#343, C₂₃×#10727, …
maximal quotient of	C₂×C₂₃×#1280, C₂₃×#7908, C₂₃×#7909, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 473);