Finite Group Databasebeta

C2×#13115188 #15864256

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115188

Splittings

SylowC13 ⋊ C2×#1880

Subgroups

subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#102C2
socleC24×C13C2×D4
prime radicalC23×D4×C13C22
cosocleC22×C4×C13C24
hypercenterC22×#102D13
hypocenterC13C2×#1880
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

2038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 170905);