Finite Group Databasebeta

C2×#13116809 #16016852

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116809

Splittings

FittingC2×C13×#350 ⋊ C2
SylowC13 ⋊ C2×#2194

Subgroups

subgroupG/H
centerC22#11718393
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#350C2
socleC22×C13#447
prime radicalC2×#11719457C2
hypercenterC2×#350D13
hypocenterC13C2×#2194
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323501);