Finite Group Databasebeta

C2×#13116435 #16015556

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

Aliases

direct productC2×#13116435

Splittings

SylowC13 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC2×C13C22×C4×C8
FrattiniC2×C8C23×D13
FittingC22×C13×M32C2
socleC23×C13C22×C8
prime radicalC24×C13C2×C8
cosocleC2×C8×C13C24
hypercenterC22×M32D13
hypocenterC13C2×#2108
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C22×M32

854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322205);