Finite Group Databasebeta

C2×#13114635 #15860616

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13114635

Splittings

FittingC2×C13×#344 ⋊ C2
SylowC13 ⋊ C2×#1757

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C13×#344C2
socleC22×C13C4×C22⋊C4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#344D13
hypocenterC13C2×#1757
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

1474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167265);