C₅×#6597 #11923899

order	1160
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#6597

Splittings

derived, Sylow	C₂₉ ⋊ C₅×C₈
Hall	C₅×C₂₉ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₅	D₂₉
commutator, hypocenter	C₂₉	C₅×C₈
Frattini	C₄	C₅×D₂₉
Fitting	C₄×C₅×C₂₉	C₂
socle, prime radical	C₂×C₅×C₂₉	C₄
cosocle	C₄×C₂₉	C₂×C₅
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₄×C₅

16 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)(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)(35,36,37,39,38,40,41,42);(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)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1160, 2);

C5×#6597 #11923899