Finite Group Databasebeta

C2×#13115457 #15865282

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

Aliases

direct productC2×#13115457

Splittings

FittingC2×C13×#336 ⋊ C2
SylowC13 ⋊ C2×#1925

Subgroups

subgroupG/H
centerC24C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#336C2
socleC24×C13C2×D4
prime radicalC23×D52C22
cosocleC22×C4×C13C24
hypercenterC2×#336D13
hypocenterC13C2×#1925
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

1454 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, 171931);