Finite Group Databasebeta

Q32×C22⋊D59 #28745413

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productQ32×C22⋊D59

Splittings

FittingC22×Q32×C59 ⋊ C2
SylowC59 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC22×Q32×C59C2
socleC22×C59C22×D8
prime radicalC2×C22⋊D59D8
hypercenterC22×Q32D59
hypocenterC59D4×Q32
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1331 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 326292);