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C5×#5774 #11756159

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

Aliases

direct productC5×#5774

Splittings

FittingC3×C5×AGL(1,ℤ/8) ⋊ C2
HallC3×C5 ⋊ #576
SylowC3 ⋊ C5×#576

Subgroups

subgroupG/H
centerC2×C5C2×D3×D4
commutator, cosocleC3×C4C24×C5
FrattiniC4C23×C5×D3
FittingC3×C5×AGL(1,ℤ/8)C2
socleC2×C3×C5C22×D4
hypercenterC5×AGL(1,ℤ/8)D3
hypocenterC3C5×#576
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×AGL(1,ℤ/8)

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

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

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80280, C5×#80939, C5×#80932, …
maximal normal subgroup ofC5×#80280, C5×#80939, C5×#80932, …
maximal quotient ofC5×#78882, C5×#78925, C5×#79210, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10354);