Finite Group Databasebeta

C2×#13116455 #16015607

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116455

Splittings

FittingC2×C13×#349 ⋊ C2
SylowC13 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C23×C8
FrattiniC2×C8C23×D13
FittingC2×C13×#349C2
socleC22×C13C2×C22⋊C8
prime radicalC22×#6127C4
cosocleC2×C8×C13C24
hypercenterC2×#349D13
hypocenterC13C2×#2115
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

1154 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, 322256);