Finite Group Databasebeta

C8×C4⋊C4×D13 #15860845

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC8×C4⋊C4×D13

Splittings

FittingC8×C13×C4⋊C4 ⋊ C2
SylowC13 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC2×C13C22×C4×C8
FrattiniC22×C4C23×D13
FittingC8×C13×C4⋊C4C2
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenterC8×C4⋊C4D13
hypocenterC13C2×C8×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167494);