Finite Group Databasebeta

C8×#4041 #12105330

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC8×#4041

Splittings

FittingC5×C8×C4⋊C4 ⋊ C2
SylowC5 ⋊ C8×#121

Subgroups

subgroupG/H
centerC22×C8C22×D5
commutatorC22×C5C23×C8
FrattiniC22×C4C23×D5
FittingC5×C8×C4⋊C4C2
socleC23×C5C23×C4
prime radicalC2×#4041C4
cosocleC22×C4×C5C24
hypercenterC8×C4⋊C4D5
hypocenterC5C8×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 175598);