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C5×#5632 #11756017

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

Aliases

direct productC5×#5632

Splittings

FittingC3×C5×C22⋊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×C22⋊Q8C2
socleC22×C3×C5C24
prime radicalC2×C5×#67C22
hypercenterC5×C22⋊Q8D3
hypocenterC3C5×D4×Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×C22⋊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)(10,12)(13,15,16,20)(14,17,18,19);(13,14,16,18)(15,19,20,17);(9,10)(11,12);(7,8)(10,12)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80771, C5×#80241, C5×#80169, …
maximal normal subgroup ofC5×#80771, C5×#80241, C5×#80169, …
maximal quotient ofC5×#73876, C5×#76614, C5×#74010, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10212);