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C5×#6599 #11923902

order1160
isoclinismisoclinic class of #1181
automorphism?
homologyAbelianization (H1) = C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC5×#6599

Splittings

derived, SylowC29 ⋊ C5×C8
HallC5×C29 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C5#1181
commutator, hypocenterC29C5×C8
FrattiniC2C5×#1181
Fitting, socle, prime radicalC2×C5×C29C4
cosocleDic29C2×C5
LCSG ▷ C29
UCSC1 ◁ C2×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 1160

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1160, 5);