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C5×#4839 #11750338

order960
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#4839

Splittings

FittingC3×C5×C4⋊C8 ⋊ C2
HallC3×C5 ⋊ #424
SylowC3 ⋊ C5×#424

Subgroups

subgroupG/H
centerC2×C4×C5C22×D3
commutatorC22×C3C22×C4×C5
FrattiniC2×C4C22×C5×D3
FittingC3×C5×C4⋊C8C2
socleC22×C3×C5C22×C4
prime radicalC22×C5×D3C2×C4
cosocleC2×C3×C4C23×C5
hypercenterC5×C4⋊C8D3
hypocenterC3C5×#424
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C5×C4⋊C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#424, C2×C5×#4839, D5×#4839, …
maximal normal subgroup ofC5×D3×#424, C2×C5×#4839, D5×#4839, …
maximal quotient ofC5×#68532, C5×#68572, C5×#68533, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4533);