Finite Group Databasebeta

#387×D37 #17997016

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct product#387×D37

Splittings

FittingC37×#387 ⋊ C2
SylowC37 ⋊ C2×#387

Subgroups

subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#387C2
socle, cosocleC23×C37C24
prime radicalC23×D37C23
hypercenter#387D37
hypocenterC37C2×#387
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #387

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6930);