Finite Group Databasebeta

#472×D37 #18004299

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

Aliases

direct product#472×D37

Splittings

FittingC37×#472 ⋊ C2
SylowC37 ⋊ C2×#472

Subgroups

subgroupG/H
centerC2#121×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#472C2
socleC2×C37C2×#121
hypercenter#472D37
hypocenterC37C2×#472
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 592

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, 14213);