Finite Group Databasebeta

D8×C22⋊#261 #16803115

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD8×C22⋊#261

Splittings

FittingC22×C13×D8 ⋊ C4
SylowC13 ⋊ C22⋊C4×D8

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC22×C13×D8C4
socleC22×C13C2×C4×D4
prime radicalC22×D8×D13C2
cosocleC2×C4×D13C24
hypercenterC22×D8#261
hypocenterC13C22⋊C4×D8
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1109764);