Finite Group Databasebeta

Q32×D73 #17989013

order4672
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D73

Splittings

FittingQ32×C73 ⋊ C2
SylowC73 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D73
commutator, cosocleC8×C73C23
FrattiniC8C22×D73
FittingQ32×C73C2
socleC2×C73C2×D8
prime radicalC2×D73D8
hypercenterQ32D73
hypocenterC73C2×Q32
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 975);