Finite Group Databasebeta

C4×#11718099 #15777947

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11718099

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
centerC2×C4×C8C2×D13
commutatorC2×C13C2×C4×C16
FrattiniC22×C8C22×D13
FittingC2×C4×C13×C16C2
socleC23×C13C22×C8
prime radicalC23×D13C2×C8
cosocleC22×C8×C13C23
hypercenterC2×C4×C16D13
hypocenterC13C4×C22⋊C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84596);