Finite Group Databasebeta

C4×#11718119 #15768121

order3328
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11718119

Splittings

SylowC13 ⋊ C4×#342

Subgroups

subgroupG/H
centerC22×C4#6103
commutatorC22×C13C43
FrattiniC25C22×D13
FittingC2×C4×C13×C22⋊C4C2
socleC23×C13C2×C22⋊C4
prime radical, cosocleC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C4×#342
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 74770);