Finite Group Databasebeta

#421×D37 #18003135

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#421×D37

Splittings

FittingC37×#421 ⋊ C2
SylowC37 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D37
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
FittingC37×#421C2
socleC2×C37C22×C22⋊C4
prime radicalC2×#41×D37C2
cosocleC2×C4×C37C24
hypercenter#421D37
hypocenterC37C2×#421
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 592

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 13049);