Finite Group Databasebeta

C2×#13128701 #16770998

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#13128701

Splittings

FittingC22×C4×Q8×C13 ⋊ C2
SylowC13 ⋊ C2×#3507

Subgroups

subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C4×Q8×C13C2
socleC23×C13C25
prime radicalC2×#11719182C2
hypercenterC22×C4×Q8D13
hypocenterC13C2×#3507
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4×Q8

7130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1077647);