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C2×#10601272 #12098748

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#10601272

Splittings

FittingC22×C5×C4⋊C8 ⋊ C2
SylowC5 ⋊ C2×#1802

Subgroups

subgroupG/H
centerC24C2×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC22×C5×C4⋊C8C2
socleC24×C5C2×D4
prime radicalC23×D20C22
cosocleC22×C4×C5C24
hypercenterC22×C4⋊C8D5
hypocenterC5C2×#1802
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

2030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 169016);