C₄×C₂₃×#124 #15669922

order	2944
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₄×C₂₃×#124

Subgroups

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

652 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);(6,7)(11,15)(13,16);(5,6,8,7)(9,10,12,14)(11,13,15,16);(5,7,8,6)(9,11)(10,13)(12,15)(14,16)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7567, C₂₃×#7584, C₂₃×#7601, …
maximal normal subgroup of	C₂₃×#7567, C₂₃×#7584, C₂₃×#7601, …
maximal quotient of	C₄×C₂₃×#388, C₄×C₂₃×#390, C₄×C₂₃×#391, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1035);

C4×C23×#124 #15669922