Finite Group Databasebeta

C8×Dic104 #15774654

order3328
isoclinismisoclinic class of D208
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic104

Splittings

SylowC13 ⋊ C8×Q32

Subgroups

subgroupG/H
centerC2×C8D104
commutatorC8×C13C22×C8
FrattiniC4×C8C22×D13
FittingC8×C13×C16C2
socle, prime radicalC22×C13C4×D8
cosocleC4×C8×C13C23
hypercenterC8×C16D13
hypocenterC13C8×Q32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C82 ◁ C8×C16

226 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 81303);