Finite Group Databasebeta

C2×#13115143 #15864113

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115143

Splittings

SylowC13 ⋊ C2×#1872

Subgroups

subgroupG/H
centerC24C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC23×C13×C4⋊C4C2
socleC24×C13C2×D4
prime radicalC25×C13D4
cosocleC22×C4×C13C24
hypercenterC23×C4⋊C4D13
hypocenterC13C2×#1872
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C4⋊C4

2270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 170762);