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C5×#5729 #11756114

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

Aliases

direct productC5×#5729

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ #544
SylowC3 ⋊ C5×#544

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×C4⋊Q8C2
socleC22×C3×C5C24
prime radicalC22×C5×D3C23
hypercenterC5×C4⋊Q8D3
hypocenterC3C5×#544
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×C4⋊Q8

412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80967, C5×#81062, #14430794, …
maximal normal subgroup ofC5×#80967, C5×#81062, #14430794, …
maximal quotient ofC5×#76195, C5×#74359, C5×#75968, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10309);