Finite Group Databasebeta

C2×#13123811 #16727371

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13123811

Splittings

FittingC22×C4×C8×C13 ⋊ C2
SylowC13 ⋊ C2×#2966

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C4×C8×C13C2
socleC23×C13C23×C4
prime radicalC2×#88184C4
cosocleC2×C4×C13C25
hypercenterC22×C4×C8D13
hypocenterC13C2×#2966
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

2070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1034020);