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C5×#4512 #11746211

order960
isoclinismisoclinic class of #4466
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#4512

Splittings

HallC3×C5 ⋊ #347
SylowC3 ⋊ C5×#347

Subgroups

subgroupG/H
centerC4×C5C4×Dic3
commutatorC3×C4C42×C5
FrattiniC2×C8C2×C5×D3
FittingC3×C5×M32C2
socleC2×C3×C5#97
prime radicalC22×C3×C5M16
cosocleC2×C3×C8C22×C5
hypercenterC5×M32D3
hypocenterC3C5×#347
LCSG ▷ C3×C4 ▷ C3
UCSC1 ◁ C4×C5 ◁ C5×M32

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#347, C2×C5×#4512, D5×#4512, …
maximal normal subgroup ofC5×D3×#347, C2×C5×#4512, D5×#4512, …
maximal quotient ofC5×#67511, C5×#67512, C5×#67811, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 406);