Finite Group Databasebeta

C2×#13113152 #15828716

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13113152

Splittings

FittingC22×C13×C22⋊C8 ⋊ C2
SylowC13 ⋊ C2×#1459

Subgroups

subgroupG/H
centerC22×C4#6103
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC23×C22⋊D13C4
cosocleC22×C4×C13C24
hypercenterC22×C22⋊C8D13
hypocenterC13C2×#1459
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135365);