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C5×#5727 #11756112

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

Aliases

direct productC5×#5727

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ D4×Q8
SylowC3 ⋊ C5×D4×Q8

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×C4⋊Q8C2
socleC22×C3×C5C24
prime radicalC2×C5×D12C22
hypercenterC5×C4⋊Q8D3
hypocenterC3C5×D4×Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×C4⋊Q8

560 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)(9,10,11,12)(13,16,17,14)(15,18,20,19);(10,12)(13,15,17,20)(14,18,16,19);(13,14,17,16)(15,19,20,18);(7,8)(10,12)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#71205, C5×#68457, #14289240, …
maximal normal subgroup ofC5×#71205, C5×#68457, #14289240, …
maximal quotient ofC5×#76614, C5×#74360, C5×#76202, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10307);