C₅×Dic₅₈ #11923915

order	1160
isoclinism	isoclinic class of Dic₅₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×Dic₅₈
unambiguous semidirect product	C₂₉⋊(C₅×Q₈)

Splittings

Hall	C₅×C₂₉ ⋊ Q₈
Sylow	C₂₉ ⋊ C₅×Q₈

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, prime radical	C₂×C₅×C₂₉	C₂²
hypercenter	C₄×C₅	D₂₉
hypocenter	C₂₉	C₅×Q₈
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1160

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5)(6,7,8,9)(10,13,12,11)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42);(6,10,8,12)(7,11,9,13)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)

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, 18);

C5×Dic58 #11923915