Finite Group Databasebeta

#322×D37 #17992870

order4736
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#322×D37

Splittings

FittingC37×#322 ⋊ C2
SylowC37 ⋊ C2×#322

Subgroups

subgroupG/H
center, FrattiniC42C22×D37
commutatorC2×C37C2×C4×C8
FittingC37×#322C2
socleC22×C37C2×C42
prime radicalC22×D37C42
cosocleC42×C37C23
hypercenter#322D37
hypocenterC37C2×#322
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C42 ◁ #322

248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2784);