Finite Group Databasebeta

Q32×D47 #15689549

order3008
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D47

Splittings

FittingQ32×C47 ⋊ C2
SylowC47 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D47
commutator, cosocleC8×C47C23
FrattiniC8C22×D47
FittingQ32×C47C2
socleC2×C47C2×D8
prime radicalC2×D47D8
hypercenterQ32D47
hypocenterC47C2×Q32
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 975);