Finite Group Databasebeta

C8×#88155 #15828504

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#88155

Splittings

FittingC2×C82×C13 ⋊ C2
SylowC13 ⋊ C8×#131

Subgroups

subgroupG/H
centerC82C2×D13
commutatorC2×C13C22×C4×C8
FrattiniC42C23×D13
FittingC2×C82×C13C2
socleC22×C13C22×C42
prime radicalC2×#6127C2×C4
cosocleC42×C13C24
hypercenterC2×C82D13
hypocenterC13C8×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C82 ◁ C2×C82

922 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, 135153);