Finite Group Databasebeta

C2×#13130592 #16797000

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13130592

Splittings

FittingC22×C13×M16 ⋊ C4
SylowC13 ⋊ C2×#1757

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC22×C13C22×C42
FrattiniC2×C4C23×#261
FittingC22×C13×M16C4
socleC22×C13C4×C22⋊C4
prime radicalC22×#6127C22
cosocleC2×C4×D13C24
hypercenterC22×M16#261
hypocenterC13C2×#1757
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

1474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103649);