Finite Group Databasebeta

C8×#88073 #15753477

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×#88073

Splittings

SylowC13 ⋊ C8×#100

Subgroups

subgroupG/H
centerC2×C8C22⋊Dic13
commutatorC22×C13C2×C4×C8
FrattiniC2×C42C22×D13
FittingC2×C8×D4×C13C2
socleC22×C13C4×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenterC2×C8×D4D13
hypocenterC13C8×#100
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×D4

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 60126);