Finite Group Databasebeta

#344×D37 #17994336

order4736
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#344×D37

Splittings

FittingC37×#344 ⋊ C2
SylowC37 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D37
commutatorC22×C37C2×C42
FrattiniC22×C4C22×D37
FittingC37×#344C2
socleC2×C37C2×#95
prime radicalC23×D37C2×C4
cosocleC22×C4×C37C23
hypercenter#344D37
hypocenterC37C2×#344
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 592

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 4250);