Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C37 ⋊ C2×C9 |
| Hall | #16864526 ⋊ C2 |
| Hall | D481 ⋊ C9 |
| Sylow | C37 ⋊ D13⋊C9 |
| Sylow | C13 ⋊ #66524⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15668367 |
| commutator, hypocenter | C13×C37 | C2×C9 |
| Fitting, socle | C3×C13×C37 | C2×C3 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,37,3|b^3=e,c^a=c^12,d^a=d^36,c^b=c^3,d^b=d^26258 conjugacy classes — view the full character table.
| maximal subgroup of | #31772752, #31772754, #22575863⋊C2, … |
| maximal normal subgroup of | #31772752, #31772754, #22575863⋊C2, … |
| maximal quotient of | #31772747, C2×#22575871 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 23);