Finite Group Databasebeta

#388×D37 #17997024

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

Aliases

direct product#388×D37

Splittings

FittingC37×#388 ⋊ C2
SylowC37 ⋊ C2×#388

Subgroups

subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#388C2
socle, cosocleC23×C37C24
prime radicalC24×D37C22
hypercenter#388D37
hypocenterC37C2×#388
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #388

928 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, 6938);