C₂×C₂₃×#341 #15669356

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₂₃×#341

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₃	D₄
commutator	C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂³×C₂₃	C₄⋊C₄
prime radical	C₂⁴×C₂₃	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(3,4)(5,6)(7,8,10,15,12,16,11,14)(9,17,18,13,20,21,19,22);(4,6)(7,9,11,19,12,20,10,18)(8,13,15,21,16,22,14,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7259, C₂₃×#7261, C₂₃×#7263, …
maximal normal subgroup of	C₂₃×#7259, C₂₃×#7261, C₂₃×#7263, …
maximal quotient of	C₂×C₂₃×#1277, C₂₃×#7872, C₂₃×#7874, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 469);

C2×C23×#341 #15669356