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C5×#4490 #11746189

order960
isoclinismisoclinic class of #826
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#4490

Splittings

HallC3×C5 ⋊ #367
SylowC3 ⋊ C5×#367

Subgroups

subgroupG/H
centerC22×C5#213
commutatorC3×C8C2×C4×C5
FrattiniC2×C8C2×C5×D3
FittingC3×C5×#107C2
socle, prime radicalC22×C3×C5D8
cosocleC2×C3×C8C22×C5
hypercenterC5×#107D3
hypocenterC3C5×#367
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#107

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#367, C2×C5×#4490, D5×#4490, …
maximal normal subgroup ofC5×D3×#367, C2×C5×#4490, D5×#4490, …
maximal quotient ofC5×#67470, C5×#67722, C5×#67579, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 384);