Finite Group Databasebeta

C8×D164 #14580403

order2624
isoclinismisoclinic class of Dic82
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC8×D164

Splittings

FittingC4×C8×C41 ⋊ C2
SylowC41 ⋊ C8×D4

Subgroups

subgroupG/H
centerC2×C8C2×D41
commutatorC2×C41C22×C8
FrattiniC2×C4C22×D41
FittingC4×C8×C41C2
socleC22×C41C22×C4
prime radicalC2×D164C4
cosocleC2×C4×C41C23
hypercenterC4×C8D41
hypocenterC41C8×D4
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C8 ◁ C4×C8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 616);