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C5×#5585 #11755970

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

Aliases

direct productC5×#5585

Splittings

FittingC3×C4×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #559
SylowC3 ⋊ C5×#559

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C4×C5×Q8C2
socleC22×C3×C5C24
prime radicalC5×#874C2
hypercenterC4×C5×Q8D3
hypocenterC3C5×#559
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×Q8

472 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)(10,14,16,15);(9,11,13,12)(10,15,16,14)(17,19,20,23)(18,21,22,24);(9,11,13,12)(10,14,16,15)(17,18,20,22)(19,24,23,21);(7,8)(9,10)(11,14)(12,15)(13,16)(19,23)(21,24)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#71031, C5×#68258, #14288868, …
maximal normal subgroup ofC5×#71031, C5×#68258, #14288868, …
maximal quotient ofC5×#73640, C5×#82462, C5×#73646, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10165);