Finite Group DatabasebetaFinite Group Databasebeta| order | 9028 |
| automorphism | Aut(G) order 9750240 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2257 |
| derived, Hall | C37×C61 ⋊ C4 |
| Sylow | C61 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2257 |
| commutator, hypocenter | C37×C61 | C4 |
| Fitting, socle | C2×C37×C61 | C2 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,61,2|a^2=d,b^a=b^36,c^a=c^602260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2257, Dic6771, #41028922, … |
| maximal normal subgroup of | C3×Dic2257, #41028922, #41028923, … |
| maximal quotient of | C3×Dic2257, Dic6771, Dic15799 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9028, 4);