Finite Group DatabasebetaFinite Group Databasebeta| order | 9906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C127 ⋊ C2×C3 |
| Hall | #19097153 ⋊ C2 |
| Hall | C13×D127 ⋊ C3 |
| Hall | D127 ⋊ C13⋊C3 |
| Sylow | C127 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ D127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C127 | C2×C3 |
| LCS | G ▷ C13×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,127|d^a=d^126,c^b=c^3,d^b=d^19287 conjugacy classes — view the full character table.
| maximal subgroup of | #23755282⋊C2, C2×#23755282, C13⋊C3×D127⋊C3, … |
| maximal normal subgroup of | #23755282⋊C2, C2×#23755282, C13⋊C3×D127⋊C3, … |
| maximal quotient of | #34090431, C2×#23755282, #44446079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9906, 16);