Finite Group Databasebeta

C2×#13112918 #15777772

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13112918

Splittings

SylowC13 ⋊ C2×#1376

Subgroups

subgroupG/H
centerC22×C8D52
commutatorC4×C13C2×C4×C8
FrattiniC22×C8C22×D13
FittingC22×C4×C8×C13C2
socleC23×C13C4⋊C8
prime radicalC24×C13M16
cosocleC22×C8×C13C23
hypercenterC22×C4×C8D13
hypocenterC13C2×#1376
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×C4×C8

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84421);