Finite Group Databasebeta

C2×#13131157 #16806975

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13131157

Splittings

FittingC22×C13×D8 ⋊ C4
SylowC13 ⋊ C2×#2145

Subgroups

subgroupG/H
centerC22C2×#88115
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC22×C13×D8C4
socleC22×C13C2×#102
prime radicalC22×#88166C2
cosocleC8×D13C24
hypercenterC22×D8#261
hypocenterC13C2×#2145
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

1170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113624);