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C5×#4990 #11750489

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

Aliases

direct productC5×#4990

Splittings

FittingC2×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ #388
SylowC3 ⋊ C5×#388

Subgroups

subgroupG/H
centerC23×C5C22×D3
commutatorC22×C3C22×C4×C5
FrattiniC23C22×C5×D3
FittingC2×C3×C5×C4⋊C4C2
socleC23×C3×C5C23
prime radicalC23×C5×D3C22
cosocleC23×C3C23×C5
hypercenterC2×C5×C4⋊C4D3
hypocenterC3C5×#388
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×C4⋊C4

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#388, C2×C5×#4990, D5×#4990, …
maximal normal subgroup ofC5×D3×#388, C2×C5×#4990, D5×#4990, …
maximal quotient ofC5×#69403, C5×#71564, C5×#69408, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4684);