Finite Group Databasebeta

#344×D73 #22609671

order9344
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#344×D73

Splittings

Fitting#344×C73 ⋊ C2
SylowC73 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D73
commutatorC22×C73C2×C42
FrattiniC22×C4C22×D73
Fitting#344×C73C2
socleC2×C73C2×#95
hypercenter#344D73
hypocenterC73C2×#344
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#344×D73, #33083439, #1757×D73, …
maximal normal subgroup ofC2×#344×D73, #33083439, #1757×D73, …
maximal quotient of#1281×D73, #32975613, #32975616, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 4250);