Finite Group Databasebeta

#367×D37 #17996374

order4736
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#367×D37

Splittings

FittingC37×#367 ⋊ C2
SylowC37 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D37
commutatorC8×C37C22×C4
FrattiniC2×C8C22×D37
FittingC37×#367C2
socleC22×C37C2×D8
prime radicalC22×D37D8
cosocleC2×C8×C37C23
hypercenter#367D37
hypocenterC37C2×#367
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

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, 6288);