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C5×#733⋊C4 #13108148

order1620
isoclinismisoclinic class of #733⋊C2
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#733⋊C4
unambiguous semidirect product#733⋊(C4×C5)

Splittings

derived, Sylow#733 ⋊ C4×C5
HallC5×#733 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC2×C5#733⋊C2
commutator, hypocenter#733C4×C5
FrattiniC2×C32C5×C3⋊D3
FittingC2×C5×#733C2
socleC2×C3×C5#272
prime radicalC2×C32×C5C3⋊D3
cosocleC2×#733C2×C5
LCSG ▷ #733
UCSC1 ◁ C2×C5

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 540

A minimal faithful permutation representation — 3 generators on 36 points:

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

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 54);