Finite Group Databasebeta

C2×#13115821 #15867559

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

Aliases

direct productC2×#13115821

Splittings

SylowC13 ⋊ C2×#1996

Subgroups

subgroupG/H
centerC23C2×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C4×C13×C22⋊C4C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#1996
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 174208);