Finite Group Databasebeta

C2×#13117017 #16017677

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13117017

Splittings

FittingC2×C13×C22⋊C16 ⋊ C2
SylowC13 ⋊ C2×#2232

Subgroups

subgroupG/H
centerC23C2×D104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×C22⋊C16C2
socleC23×C13C2×D8
prime radicalC2×#11718776C2
hypercenterC2×C22⋊C16D13
hypocenterC13C2×#2232
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 324326);