Finite Group Databasebeta

C2×#13129709 #16779704

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13129709

Splittings

FittingC22×C13×C4⋊C4 ⋊ C4
SylowC13 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC24C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC24×C13C22⋊C4
prime radicalC24×D13D4
cosocleC22×C4×D13C23
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1294
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1086353);