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C2×#10600253 #12101436

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#10600253

Splittings

SylowC5 ⋊ C2×#1920

Subgroups

subgroupG/H
centerC24C2×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C4×C5×C4⋊C4C2
socle, prime radicalC24×C5C2×D4
cosocleC22×C4×C5C24
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C2×#1920
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

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, 171704);