Finite Group Databasebeta

Q8×C22⋊C4×D73 #33245169

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productQ8×C22⋊C4×D73

Splittings

FittingQ8×C22⋊C4×C73 ⋊ C2
SylowC73 ⋊ C2×Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingQ8×C22⋊C4×C73C2
socle, cosocleC23×C73C25
prime radicalC24×D73C23
hypercenterQ8×C22⋊C4D73
hypocenterC73C2×Q8×C22⋊C4
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

5414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 328753);