Finite Group Databasebeta

C2×#13129674 #16779141

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13129674

Splittings

SylowC13 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC24C22⋊#261
commutatorC22×C13C2×C4×C8
FrattiniC24C22×#261
FittingC24×C4×C13C4
socleC24×C13C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×Dic13C23
hypercenterC24×C4#261
hypocenterC13C2×#1280
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C25 ◁ C24×C4

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1085790);