Finite Group Databasebeta

#428×D37 #18003177

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#428×D37

Splittings

FittingC37×#428 ⋊ C2
SylowC37 ⋊ C2×#428

Subgroups

subgroupG/H
centerC22C2×D4×D37
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
FittingC37×#428C2
socleC22×C37C22×D4
prime radicalC23×D37D4
cosocleC2×C4×C37C24
hypercenter#428D37
hypocenterC37C2×#428
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

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, 13091);