Finite Group Databasebeta

C8×#88180 #15861122

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#88180

Splittings

SylowC13 ⋊ C8×#117

Subgroups

subgroupG/H
centerC2×C4×C8C2×D13
commutatorC2×C13C22×C4×C8
FrattiniC22×C4C23×D13
FittingC22×C4×C8×C13C2
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C8×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167771);