Finite Group Databasebeta

Q32×C22⋊D13 #16019643

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productQ32×C22⋊D13

Splittings

FittingC22×C13×Q32 ⋊ C2
SylowC13 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC22×C13×Q32C2
socleC22×C13C22×D8
prime radicalC2×C22⋊D13D8
hypercenterC22×Q32D13
hypocenterC13D4×Q32
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 326292);