Finite Group Databasebeta

#473×D37 #18004305

order4736
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#473×D37

Splittings

FittingC37×#473 ⋊ C2
SylowC37 ⋊ C2×#473

Subgroups

subgroupG/H
centerC2#121×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#473C2
socleC2×C37C2×#121
prime radical#41×D37C22
hypercenter#473D37
hypocenterC37C2×#473
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 14219);