C₂₃×C₄⋊C₃₂ #15669040

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₃×C₄⋊C₃₂
unambiguous semidirect product	C₄⋊(C₂₃×C₃₂)

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₂₃	C₂²
commutator	C₂	C₂×C₂₃×C₃₂
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
socle, prime radical	C₂²×C₂₃	C₂×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₂₃ ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 2 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29,30,34,31,35,38,44,32,36,39,45,41,47,50,54,33,37,40,46,42,48,51,55,43,49,52,56,53,57,58,59);(24,25,26,27)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×D₄⋊C₃₂, C₂₃×#7380, C₂₃×Q₈⋊C₃₂, …
maximal normal subgroup of	C₂₃×D₄⋊C₃₂, C₂₃×#7380, C₂₃×Q₈⋊C₃₂, …
maximal quotient of	C₂₃×#7455, C₂₃×#7458, C₂₃×#7465, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 153);

C23×C4⋊C32 #15669040