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C5×#4565 #11746264

order960
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#4565

Splittings

HallC3×C5 ⋊ #362
SylowC3 ⋊ C5×#362

Subgroups

subgroupG/H
centerC2×C5#832
commutatorC3×C8C2×C4×C5
FrattiniC2×C8C2×C5×D3
FittingC2×C3×C5×Q16C2
socleC2×C3×C5#102
prime radicalC22×C3×C5SD16
cosocleC2×C3×C8C22×C5
hypercenterC2×C5×Q16D3
hypocenterC3C5×#362
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C2×C5×Q16

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(6,7,8)(9,11,14,23)(10,15,19,32)(12,24,26,21)(13,28,29,38)(16,31,18,30)(17,34,35,36)(20,27,37,33)(22,25,39,40);(7,8)(9,10,12,16,14,19,26,18)(11,20,21,34,23,37,24,36)(13,27,25,17,29,33,40,35)(15,28,30,22,32,38,31,39)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#362, C2×C5×#4565, D5×#4565, …
maximal normal subgroup ofC5×D3×#362, C2×C5×#4565, D5×#4565, …
maximal quotient ofC5×#67764, C5×#67777, C5×#67793, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 459);