C₅×D₁₁₆ #11923917

order	1160
isoclinism	isoclinic class of Dic₅₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₁₁₆
unambiguous semidirect product	C₄⋊(C₅×D₂₉)

Splittings

Fitting	C₄×C₅×C₂₉ ⋊ C₂
Hall	C₅×C₂₉ ⋊ D₄
Sylow	C₂₉ ⋊ C₅×D₄

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×D₂₉
commutator, cosocle	C₂×C₂₉	C₂²×C₅
Frattini	C₂	C₂×C₅×D₂₉
Fitting	C₄×C₅×C₂₉	C₂
socle	C₂×C₅×C₂₉	C₂²
hypercenter	C₄×C₅	D₂₉
hypocenter	C₂₉	C₅×D₄
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 580

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1160, 20);

C5×D116 #11923917