Finite Group Databasebeta

C2×D13×#361 #16015868

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D13×#361

Splittings

FittingC2×C13×#361 ⋊ C2
SylowC13 ⋊ C22×#361

Subgroups

subgroupG/H
centerC22D13×#102
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C13×#361C2
socleC22×C13C2×#102
prime radicalC22×D8×D13C2
cosocleC2×C8×C13C24
hypercenterC2×#361D13
hypocenterC13C22×#361
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322517);