Finite Group Databasebeta

#449×D71 #22597537

order9088
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#449×D71

Splittings

Fitting#449×C71 ⋊ C2
SylowC71 ⋊ C2×#449

Subgroups

subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#449×C71C2
socleC22×C71C22×D4
hypercenter#449D71
hypocenterC71C2×#449
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

812 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#449×D71, #3002×D71, #3005×D71, …
maximal normal subgroup ofC2×#449×D71, #3002×D71, #3005×D71, …
maximal quotient of#1597×D71, #1609×D71, #1600×D71, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 13707);