Finite Group Databasebeta

C2×#13114673 #15860749

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13114673

Splittings

FittingC22×C4×C8×C13 ⋊ C2
SylowC13 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC22×C8D52
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC22×C4×C8×C13C2
socleC23×C13C4×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×#1764
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×C4×C8

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 167398);