C₄×C₂₃×#123 #15669920

order	2944
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄×C₂₃×#123

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

688 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);(6,8)(10,13)(11,15);(9,10)(11,14)(12,13)(15,16);(5,6)(7,8)(9,11,12,15)(10,14,13,16)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#8966, C₂₃×#8968, C₂₃×#11472, …
maximal normal subgroup of	C₂₃×#8966, C₂₃×#8968, C₂₃×#11472, …
maximal quotient of	C₄×C₂₃×#386, C₄×C₂₃×#388, C₄×C₂₃×#385, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1033);

C4×C23×#123 #15669920