Finite Group Databasebeta

C8×#88137 #15869876

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#88137

Splittings

FittingC8×C13×C22⋊C4 ⋊ C2
SylowC13 ⋊ C8×#123

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC8×C13×C22⋊C4C2
socleC23×C13C23×C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenterC8×C22⋊C4D13
hypocenterC13C8×#123
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C8×C22⋊C4

1034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 176525);