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C5×#5465 #11755476

order960
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#5465

Splittings

Fitting, HallC5×H(3,𝔽4) ⋊ C3
derived, SylowH(3,𝔽4) ⋊ C3×C5

Subgroups

subgroupG/H
center, socle, hypercenterC22×C5C22⋊A4
commutator, cosocle, hypocenterH(3,𝔽4)C3×C5
FrattiniC22C5×C22⋊A4
FittingC5×H(3,𝔽4)C3
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C22×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC5⋊#85556, C5⋊#85557, C5⋊#85560, …
maximal subgroup ofC5×#2202⋊C3, C5×#85556, C5×#85557, …
maximal normal subgroup ofC5×#2202⋊C3, C5×#85556, C5×#85557, …
maximal quotient ofC5×#73291, C5×#73293, C2×C5×#5465

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9671);