Finite Group Databasebeta

C2×#13129673 #16779140

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13129673

Splittings

FittingC2×C13×C22⋊C8 ⋊ C4
SylowC13 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC22×C13C2×C4×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊C8C4
socleC23×C13#95
prime radicalC24×D13C2×C4
cosocleC22×C4×D13C23
hypercenterC2×C22⋊C8#261
hypocenterC13C2×#1280
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1085789);