Finite Group Databasebeta

C8×#88055 #15752269

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct productC8×#88055

Splittings

SylowC13 ⋊ C8×#97

Subgroups

subgroupG/H
centerC2×C4×C8C2×D13
commutatorC2×C13C42×C8
FrattiniC2×C42C22×D13
FittingC2×C82×C13C2
socle, prime radicalC23×C13C2×C42
cosocleC2×C42×C13C23
hypercenterC2×C82D13
hypocenterC13C8×#97
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4×C8 ◁ C2×C82

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

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, 58918);