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C5×#63372 #13083815

order1440
isoclinismisoclinic class of Dic36
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63372

Splittings

HallC5×C9 ⋊ #108
SylowC9 ⋊ C5×#108

Subgroups

subgroupG/H
centerC4×C5D36
commutatorC4×C9C2×C4×C5
FrattiniC2×C3×C4C2×C5×D3
FittingC2×C5×C8×C9C2
socleC2×C3×C5C4⋊Dic3
prime radicalC22×C3×C5Dic6
cosocleC2×C4×C9C22×C5
hypercenterC2×C5×C8D9
hypocenterC9C5×#108
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×C8

90 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)(6,7,10,12,14,13,8,11,9)(15,17,19,26,20,27,18,25)(16,21,22,24,23,29,28,30);(7,9)(8,12)(10,11)(13,14)(15,16,18,22,20,23,19,28)(17,24,25,29,27,30,26,21)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 132);