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C5×#4496 #11746195

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

Aliases

direct productC5×#4496

Splittings

HallC3×C5 ⋊ #362
SylowC3 ⋊ C5×#362

Subgroups

subgroupG/H
centerC2×C5#809
commutatorC3×C8C2×C4×C5
FrattiniC2×C8C2×C5×D3
FittingC3×C5×#108C2
socleC2×C3×C5#102
prime radicalC22×C3×C5SD16
cosocleC2×C3×C8C22×C5
hypercenterC5×#108D3
hypocenterC3C5×#362
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#108

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#362, C2×C5×#4496, D5×#4496, …
maximal normal subgroup ofC5×D3×#362, C2×C5×#4496, D5×#4496, …
maximal quotient ofC5×#67466, C5×#67488, C5×#67474, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 390);