C₅×Dic₂₃ #90744

order	460
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×Dic₂₃
unambiguous semidirect product	C₂₃⋊(C₄×C₅)

Splittings

derived, Sylow	C₂₃ ⋊ C₄×C₅
Hall	C₅×C₂₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₂₃
commutator, hypocenter	C₂₃	C₄×C₅
Frattini	C₂	C₅×D₂₃
Fitting, socle, prime radical	C₂×C₅×C₂₃	C₂
cosocle	C₂×C₂₃	C₂×C₅
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₅

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 460

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×Dic₂₃, #11745064, #11745067, …
maximal normal subgroup of	D₅×Dic₂₃, #11745064, #11745067, …
maximal quotient of	C₅×C₂₃⋊C₈, C₂×C₅×Dic₂₃, C₃×C₅×Dic₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(460, 2);

C5×Dic23 #90744

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₅×Dic₂₃ #90744