Finite Group Databasebeta

C2×#13130630 #16797126

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13130630

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C2×#1770

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC23×C13C2×C42
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenterC2×C4×C8#261
hypocenterC13C2×#1770
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103775);