Finite Group Databasebeta

C2×#13116431 #16015552

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13116431

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC22×C16C2×D13
commutatorC2×C13C22×C4×C8
FrattiniC2×C8C23×D13
FittingC2×C4×C13×C16C2
socleC23×C13C22×C8
prime radicalC23×D13C2×C8
cosocleC2×C8×C13C24
hypercenterC2×C4×C16D13
hypocenterC13C2×#2108
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

854 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, 322201);