C₄×C₂₃×#117 #15669889

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₃ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₄×C₂₃×#117

Subgroups

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

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7854, C₂₃×#7856, C₂₃×#7866, …
maximal normal subgroup of	C₂₃×#7854, C₂₃×#7856, C₂₃×#7866, …
maximal quotient of	C₄×C₂₃×#376, C₄²×C₂²⋊C₄×C₂₃, C₄²×C₄⋊C₄×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1002);

C4×C23×#117 #15669889