Finite Group Databasebeta

C2×#10598206 #11989587

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10598206

Splittings

SylowC5 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic5
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC2×C5×#423C2
socleC23×C5#95
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenterC2×#423D5
hypocenterC5C2×#1303
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#423

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 59855);