Finite Group Databasebeta

C23×C22⋊Dic37 #18007754

order4736
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊Dic37

Splittings

SylowC37 ⋊ C23×C22⋊C4

Subgroups

subgroupG/H
centerC25C2×D37
commutatorC2×C37C24×C4
FrattiniC22C24×D37
Fitting, prime radicalC26×C37C2
socleC25×C37C22
cosocleC22×C37C25
hypercenterC26D37
hypocenterC37C23×C22⋊C4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C25 ◁ C26

4632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 17668);