Finite Group Databasebeta

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C5×#63387 #13083830

order1440
isoclinismisoclinic class of #63385
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63387

Splittings

FittingC5×C9×Q16 ⋊ C2
HallC5×C9 ⋊ SD32
SylowC9 ⋊ C5×SD32

Subgroups

subgroupG/H
centerC2×C5#3673
commutator, cosocleC8×C9C22×C5
FrattiniC3×C8C2×C5×D3
FittingC5×C9×Q16C2
socleC2×C3×C5#213
prime radicalC5×D72C2
hypercenterC5×Q16D9
hypocenterC9C5×SD32
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×Q16

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5)(6,14,9,12,11,10,8,7,13)(15,16,19,22)(17,24,26,30)(18,27,25,21)(20,28,29,23);(7,9)(8,12)(10,11)(13,14)(16,20)(17,23)(18,25)(21,30)(22,29)(24,27)(26,28)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 147);