Finite Group Databasebeta

Q32×C22⋊D73 #33242708

order18688
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productQ32×C22⋊D73

Splittings

FittingC22×Q32×C73 ⋊ C2
SylowC73 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C2×D8×D73
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC22×Q32×C73C2
socleC22×C73C22×D8
prime radicalC2×C22⋊D73D8
hypercenterC22×Q32D73
hypocenterC73D4×Q32
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

1639 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 326292);