Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C37 ⋊ C2×C9 |
| Hall | #16864530 ⋊ C2 |
| Hall | D481 ⋊ C9 |
| Sylow | C37 ⋊ D13⋊C9 |
| Sylow | C13 ⋊ #66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C37 | C2×C9 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,13,37|b^3=c,d^a=d^12,e^a=e^36,d^b=d^3,e^b=e^34,e^c=e^1050 conjugacy classes — view the full character table.
| maximal subgroup of | #31772888, #31772890, #22575876⋊C2, … |
| maximal normal subgroup of | #31772888, #31772890, #22575876⋊C2, … |
| maximal quotient of | #31772828, C2×#22575876 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 28);