Finite Group Databasebeta

C2×#13116643 #16015994

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#13116643

Splittings

SylowC13 ⋊ C2×#2164

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC22×C13C23×C8
FrattiniC2×C8C23×D13
FittingC2×C13×#405C2
socleC23×C13C22×C8
prime radicalC24×C13C2×C8
cosocleC2×C8×C13C24
hypercenterC2×#405D13
hypocenterC13C2×#2164
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×#405

610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322643);