Finite Group Databasebeta

#468×D37 #18004180

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

Aliases

direct product#468×D37

Splittings

FittingC37×#468 ⋊ C2
SylowC37 ⋊ C2×#468

Subgroups

subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#468C2
socleC22×C37C22×D4
prime radical#121×D37C2
hypercenter#468D37
hypocenterC37C2×#468
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

544 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, 14094);