Finite Group Databasebeta

C2×C4×Dic82 #14580801

order2624
isoclinismisoclinic class of Dic82
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic82

Splittings

SylowC41 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D41
commutatorC2×C41C23×C4
FrattiniC22C23×D41
FittingC2×C42×C41C2
socle, prime radicalC23×C41C23
cosocleC22×C41C24
hypercenterC2×C42D41
hypocenterC41C2×C4×Q8
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2624

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, 1014);