Finite Group Databasebeta

C4×#11718565 #16016203

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11718565

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C4×#508

Subgroups

subgroupG/H
centerC42D104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C4×C13×C16C2
socleC22×C13C22×D8
prime radicalC2×#11718565C2
cosocleC2×C8×C13C24
hypercenterC2×C4×C16D13
hypocenterC13C4×#508
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

690 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, 322852);