Finite Group Databasebeta

C2×C4×Dic718 #37526908

order22976
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic718

Splittings

SylowC359 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D359
commutatorC2×C359C23×C4
FrattiniC22C23×D359
FittingC2×C42×C359C2
socle, prime radicalC23×C359C23
cosocleC22×C359C24
hypercenterC2×C42D359
hypocenterC359C2×C4×Q8
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22976

Conjugacy classes & character table

5768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 1014);