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C5×#5567 #11755952

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

Aliases

direct productC5×#5567

Splittings

HallC3×C5 ⋊ #557
SylowC3 ⋊ C5×#557

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C4×C5×Q8C2
socle, prime radicalC22×C3×C5C24
hypercenterC4×C5×Q8D3
hypocenterC3C5×#557
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×Q8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#71034, C5×#68265, #14289183, …
maximal normal subgroup ofC5×#71034, C5×#68265, #14289183, …
maximal quotient ofC5×C4⋊C4×Dic6, C5×#73637, C5×#73641, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10147);