Finite Group Databasebeta

C2×#13113281 #15829339

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13113281

Splittings

FittingC2×C13×Q8⋊C8 ⋊ C2
SylowC13 ⋊ C2×#1491

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×Q8⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC42×C13C24
hypercenterC2×Q8⋊C8D13
hypocenterC13C2×#1491
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

1302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135988);