Finite Group Databasebeta

C22×#65014 #12963129

order1280
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×#65014

Splittings

FittingC22×C5×C22⋊C8 ⋊ C2
SylowC5 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutatorC2×C5C24×C8
FrattiniC2×C4C24×D5
FittingC22×C5×C22⋊C8C2
socleC24×C5C22×C4
prime radicalC23×C22⋊D5C4
cosocleC2×C4×C5C25
hypercenterC22×C22⋊C8D5
hypocenterC5C22×C8×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1033397);