Finite Group Databasebeta

C8×Dic718 #37526568

order22976
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic718

Splittings

SylowC359 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×D359
commutatorC2×C359C22×C8
FrattiniC2×C4C22×D359
FittingC4×C8×C359C2
socle, prime radicalC22×C359C22×C4
cosocleC2×C4×C359C23
hypercenterC4×C8D359
hypocenterC359C8×Q8
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C2×C8 ◁ C4×C8

102 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, 674);