Finite Group Databasebeta

#417×D37 #18003104

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

Aliases

direct product#417×D37

Splittings

FittingC37×#417 ⋊ C2
SylowC37 ⋊ C2×#417

Subgroups

subgroupG/H
centerC22C2×D4×D37
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
FittingC37×#417C2
socleC22×C37C22×D4
prime radicalC2×#41×D37C2
cosocleC2×C4×C37C24
hypercenter#417D37
hypocenterC37C2×#417
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

816 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, 13018);