Finite Group Databasebeta

C2×#10598622 #13025520

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

Aliases

direct productC2×#10598622

Splittings

SylowC5 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#4007
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC2×C5×#107C4
socleC23×C5#102
prime radicalC23×D5SD16
cosocleC2×C8×D5C23
hypercenterC2×#107AGL(1,𝔽5)
hypocenterC5C2×#1387
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1095788);