Finite Group DatabasebetaFinite Group Databasebeta| order | 9513 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C151 ⋊ C9 |
| Sylow | C151 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C151⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15691748 |
| commutator, hypocenter | C7×C151 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C151 | C3 |
| LCS | G ▷ C7×C151 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,151,3|a^3=d,b^a=b^2,c^a=c^321065 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#23748878, #34039752, #34039756, … |
| maximal normal subgroup of | C2×#23748878, #34039752, #34039756, … |
| maximal quotient of | C2×#23748878, C22⋊#23748878 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9513, 4);