C₂₉×Dic₁₀ #11923920

order	1160
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×Dic₁₀
unambiguous semidirect product	C₅⋊(Q₈×C₂₉)

Splittings

Hall	C₅×C₂₉ ⋊ Q₈
Sylow	C₅ ⋊ Q₈×C₂₉

Subgroups

	subgroup	G/H
center	C₂×C₂₉	C₂×D₅
commutator, cosocle	C₂×C₅	C₂²×C₂₉
Frattini	C₂	C₂×D₅×C₂₉
Fitting	C₄×C₅×C₂₉	C₂
socle, prime radical	C₂×C₅×C₂₉	C₂²
hypercenter	C₄×C₂₉	D₅
hypocenter	C₅	Q₈×C₂₉
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₂₉ ◁ C₄×C₂₉

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1160, 23);

C29×Dic10 #11923920