Finite Group Databasebeta

#344×D47 #20243128

order6016
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#344×D47

Splittings

FittingC47×#344 ⋊ C2
SylowC47 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D47
commutatorC22×C47C2×C42
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47C2×#95
hypercenter#344D47
hypocenterC47C2×#344
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

550 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#344×D47, #26213733, D47×#1757, …
maximal normal subgroup ofC2×#344×D47, #26213733, D47×#1757, …
maximal quotient ofD47×#1281, #26105907, #26105910, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6016, 4250);