Finite Group DatabasebetaFinite Group Databasebeta| order | 9028 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C61 ⋊ C4 |
| Sylow | C61 ⋊ #3866 |
| Sylow | C37 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C61 | C4 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,37,61|a^2=b,c^a=c^31,d^a=d^50,c^b=c^36,d^b=d^60568 conjugacy classes — view the full character table.
| maximal subgroup of | #41028929, #41028930, #41028935, … |
| maximal normal subgroup of | #41028929, #41028930, #41028935, … |
| maximal quotient of | C3×#22583259, C3⋊#22583259 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9028, 8);