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C₂×C₂₃×#428 #15670529

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₂₃×#428

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂×D₄
commutator	C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂⁴×C₂₃	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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);(3,4,5,6)(8,11)(9,13)(12,14);(7,8,9,11,10,12,13,14);(8,12)(11,14)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10896, C₂₃×#10899, C₂₃×#10903, …
maximal normal subgroup of	C₂₃×#10896, C₂₃×#10899, C₂₃×#10903, …
maximal quotient of	C₂×C₂₃×#1565, C₂×C₂₃×#1569, C₂₃×#17796, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1642);