Finite Group Databasebeta

C8×#88237 #16797267

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#88237

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C8×#117

Subgroups

subgroupG/H
centerC4×C8C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC22×C13C22×C42
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenterC2×C4×C8#261
hypocenterC13C8×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103916);