Finite Group Databasebeta

#103×Dic37 #17994418

order4736
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#103×Dic37

Splittings

SylowC37 ⋊ C4×#103

Subgroups

subgroupG/H
centerC23D4×D37
commutatorC4×C37C2×C42
FrattiniC22×C4C22×D37
FittingC2×#103×C37C2
socle, prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenterC2×#103D37
hypocenterC37C4×#103
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

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, 4332);