Finite Group Databasebeta

C4×#11718101 #15778124

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11718101

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C4×#357

Subgroups

subgroupG/H
centerC22×C4D104
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C4×C13×C16C2
socleC23×C13C2×D8
prime radicalC22×D104C22
cosocleC22×C8×C13C23
hypercenterC2×C4×C16D13
hypocenterC13C4×#357
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84773);