Finite Group Databasebeta

C2×#13131088 #16806810

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

Aliases

direct productC2×#13131088

Splittings

FittingC2×C13×#120 ⋊ C4
SylowC13 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC22D13⋊#99
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C13×#120C4
socleC22×C13C2×#99
prime radicalC2×#11719291C2
cosocleC2×C22⋊D13C24
hypercenterC2×#120#261
hypocenterC13C2×#2120
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#120

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113459);