Finite Group Databasebeta

C4×#11718793 #15860597

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

Aliases

direct productC4×#11718793

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ C4×#413

Subgroups

subgroupG/H
centerC42#6103
commutatorC22×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C4×C13×M16C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×C4×M16D13
hypocenterC13C4×#413
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

1570 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, 167246);