Finite Group Databasebeta

Q32×Dic73 #22611790

order9344
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productQ32×Dic73

Splittings

SylowC73 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC22D8×D73
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
FittingC2×Q32×C73C2
socleC22×C73C2×D8
hypercenterC2×Q32D73
hypocenterC73C4×Q32
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#33006560, SD64×Dic73, #33006567, …
maximal normal subgroup of#33006560, SD64×Dic73, #33006567, …
maximal quotient ofQ32×#10596831, #32997901, #32997975, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 6369);