Finite Group Databasebeta

C2×#13117512 #16021655

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13117512

Splittings

FittingC22×C4×Q8×C13 ⋊ C2
SylowC13 ⋊ C2×#2323

Subgroups

subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C4×Q8×C13C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC22×C4×Q8D13
hypocenterC13C2×#2323
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×Q8

3198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 328304);