Finite Group DatabasebetaFinite Group Databasebeta| order | 17325 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9×C11 · Schur multiplier (H2) = C5 |
| direct product | C52×C11×C7⋊C9 |
| unambiguous semidirect product | C7⋊(C52×C9×C11) |
| unambiguous semidirect product | (C5×C7)⋊(C5×C9×C11) |
| derived, Sylow | C7 ⋊ C52×C9×C11 |
| Hall | C52×C7×C11 ⋊ C9 |
| Hall | C52×C7 ⋊ C9×C11 |
| Hall | C7×C11 ⋊ C52×C9 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17325 |
4125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×C11×D7⋊C9, C52×C11⋊(D7⋊C9), C52×D11×C7⋊C9, … |
| maximal normal subgroup of | C52×C11×D7⋊C9, C52×C11⋊(D7⋊C9), C52×D11×C7⋊C9, … |
| maximal quotient of | C2×C52×C11×C7⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17325, 12);