Finite Group Databasebeta

C2×#13114667 #15860683

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

Aliases

direct productC2×#13114667

Splittings

SylowC13 ⋊ C2×#1763

Subgroups

subgroupG/H
centerC24C2×D52
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC22×C13×#97C2
socle, prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC22×#97D13
hypocenterC13C2×#1763
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

1686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167332);