Finite Group Databasebeta

C2×#13123890 #16727676

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13123890

Splittings

FittingC22×C13×C22⋊C8 ⋊ C2
SylowC13 ⋊ C2×#2977

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×C22⋊C8C2
socleC23×C13C23×C4
prime radicalC2×#11719496C2
cosocleC2×C4×C13C25
hypercenterC22×C22⋊C8D13
hypocenterC13C2×#2977
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8

2362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1034325);