Finite Group Databasebeta

#376×D37 #17996921

order4736
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#376×D37

Splittings

FittingC37×#376 ⋊ C2
SylowC37 ⋊ C2×#376

Subgroups

subgroupG/H
centerC22×C4C22×D37
commutatorC2×C37C22×C42
FrattiniC23C23×D37
FittingC37×#376C2
socle, cosocleC23×C37C24
prime radicalC23×D37C23
hypercenter#376D37
hypocenterC37C2×#376
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ #376

840 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, 6835);