Finite Group Databasebeta

#533×D37 #18007881

order4736
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#533×D37

Splittings

FittingC37×#533 ⋊ C2
SylowC37 ⋊ C2×#533

Subgroups

subgroupG/H
centerC2×C4C23×D37
commutator, socle, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC37×#533C2
prime radicalC23×D37C23
hypercenter#533D37
hypocenterC37C2×#533
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ #533

1168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 17795);