Finite Group Databasebeta

#432×D37 #18003213

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#432×D37

Splittings

FittingC37×#432 ⋊ C2
SylowC37 ⋊ C2×#432

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D37
commutator, socleC22×C37C23×C4
FittingC37×#432C2
prime radicalC23×D37C2×C4
cosocleC2×C4×C37C24
hypercenter#432D37
hypocenterC37C2×#432
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ #432

488 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, 13127);