Finite Group Databasebeta

C2×#13115747 #15866914

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13115747

Splittings

SylowC13 ⋊ C2×#1978

Subgroups

subgroupG/H
centerC23#88192
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC23×C13×D8C2
socleC23×C13#121
cosocleC22×C4×C13C24
hypercenterC23×D8D13
hypocenterC13C2×#1978
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

1694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 173563);