Finite Group Databasebeta

C2×#13131133 #16806916

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

Aliases

direct productC2×#13131133

Splittings

SylowC13 ⋊ C2×#2133

Subgroups

subgroupG/H
centerC22C2×#88107
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC22×#6127C4
cosocleC2×Dic26C24
hypercenterC2×#117#261
hypocenterC13C2×#2133
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

1198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

166 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113565);