Finite Group Databasebeta

C2×D13×D4⋊C8 #15829259

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

Aliases

direct productC2×D13×D4⋊C8

Splittings

FittingC2×C13×D4⋊C8 ⋊ C2
SylowC13 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C23×C8
FrattiniC42C23×D13
FittingC2×C13×D4⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×D13C4
cosocleC42×C13C24
hypercenterC2×D4⋊C8D13
hypocenterC13C22×D4⋊C8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135908);