Finite Group Databasebeta

C2×#13131192 #16807036

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13131192

Splittings

SylowC13 ⋊ C2×#2161

Subgroups

subgroupG/H
centerC22C2×#88102
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC2×C13×M32C4
socleC22×C13C2×#107
prime radicalC23×D13Q16
cosocleC8×D13C24
hypercenterC2×M32#261
hypocenterC13C2×#2161
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113685);