Finite Group Databasebeta

D8×#11924029 #33967392

order18688
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD8×#11924029

Splittings

FittingQ8×D8×C73 ⋊ C2
SylowC73 ⋊ D8×#41

Subgroups

subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingQ8×D8×C73C2
socleC22×C73C23×D4
hypercenterQ8×D8D73
hypocenterC73D8×#41
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q8×D8

2406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1050976);