Finite Group Databasebeta

C2×#13130571 #16796908

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13130571

Splittings

FittingC2×C13×C22⋊C8 ⋊ C4
SylowC13 ⋊ C2×C8×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC2×C13×C22⋊C8C4
socleC23×C13C2×C42
prime radicalC24×D13C2×C4
cosocleC2×C4×D13C24
hypercenterC2×C22⋊C8#261
hypocenterC13C2×C8×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103557);