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C22⋊C4×#711 #12258497

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22⋊C4×#711

Splittings

FittingC5×D4×C22⋊C4 ⋊ C2
SylowC5 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
center, FrattiniC23C24×D5
commutatorC22×C5C24×C4
FittingC5×D4×C22⋊C4C2
socle, cosocleC23×C5C25
prime radicalC23×#711C2
hypercenterD4×C22⋊C4D5
hypocenterC5C22⋊C4×#41
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ D4×C22⋊C4

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 328765);