Finite Group Databasebeta

C2×#13117175 #16021102

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×#13117175

Splittings

FittingC2×C13×#376 ⋊ C2
SylowC13 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC2×C13C23×C42
FrattiniC23C24×D13
FittingC2×C13×#376C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC2×#376D13
hypocenterC13C2×C4×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×#376

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327751);