Finite Group Databasebeta

C2×D13⋊#361 #16806980

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

Aliases

direct productC2×D13⋊#361
unambiguous semidirect productD13⋊(C2×#361)

Splittings

SylowC13 ⋊ C22×#361

Subgroups

subgroupG/H
centerC22C2×#88115
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC22×C13×D8C4
socleC22×C13C2×#102
prime radicalC22×D8×D13C2
cosocleC8×D13C24
hypercenterC22×D8#261
hypocenterC13C22×#361
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113629);