Finite Group Databasebeta

C4×#11718100 #15777968

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11718100

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C4×#350

Subgroups

subgroupG/H
centerC4×C8D52
commutatorC4×C13C2×C4×C8
FrattiniC22×C8C22×D13
FittingC2×C4×C13×C16C2
socleC22×C13C2×C22⋊C8
prime radicalC2×#6127C2×C4
cosocleC22×C8×C13C23
hypercenterC2×C4×C16D13
hypocenterC13C4×#350
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C2×C4×C16

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84617);