Finite Group Databasebeta

C2×#13113198 #15828888

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

Aliases

direct productC2×#13113198

Splittings

FittingC2×C13×#324 ⋊ C2
SylowC13 ⋊ C2×#1472

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#324C2
socleC23×C13C2×C22⋊C4
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenterC2×#324D13
hypocenterC13C2×#1472
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

1426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135537);