C₅×C₂²⋊D₂₉ #11923919

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

Aliases

direct product	C₅×C₂²⋊D₂₉
unambiguous semidirect product	C₂²⋊(C₅×D₂₉)

Splittings

Fitting	C₂²×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	C₂²×C₅×C₂₉	C₂
socle	C₂×C₅×C₂₉	C₂²
hypercenter	C₂²×C₅	D₂₉
hypocenter	C₂₉	C₅×D₄
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×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)(6,7,9,11,13,15,17,19,21,23,25,27,29,31,33,34,32,30,28,26,24,22,20,18,16,14,12,10,8)(36,38);(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)

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, 22);

C5×C22⋊D29 #11923919