Finite Group Databasebeta

C2×#13123474 #16726650

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#13123474

Splittings

SylowC13 ⋊ C2×#2921

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#117C2
socleC23×C13C23×C4
prime radicalC25×C13C2×C4
cosocleC2×C4×C13C25
hypercenterC22×#117D13
hypocenterC13C2×#2921
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×#117

2198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033299);