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C5×#5817 #11756202

order960
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#5817

Splittings

FittingC22×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #548
SylowC3 ⋊ C5×#548

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC22×C3×C5×Q8C2
socleC22×C3×C5C24
hypercenterC22×C5×Q8D3
hypocenterC3C5×#548
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C5×Q8

580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80060, C5×#83864, #14453506, …
maximal normal subgroup ofC5×#80060, C5×#83864, #14453506, …
maximal quotient ofC5×Q8×#217, C5×#82457, C5×#82461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10397);