Finite Group Databasebeta

C8×#88063 #15753478

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

Aliases

direct productC8×#88063

Splittings

FittingC8×C13×M16 ⋊ C2
SylowC13 ⋊ C8×#100

Subgroups

subgroupG/H
centerC2×C8#6103
commutatorC22×C13C2×C4×C8
FrattiniC2×C42C22×D13
FittingC8×C13×M16C2
socleC22×C13C4×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenterC8×M16D13
hypocenterC13C8×#100
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C8×M16

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, 60127);