Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×ΓL(1,𝔽25) |
| Fitting | C3×C8×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ M16 |
| Sylow | C3 ⋊ M16×C19 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×ΓL(1,𝔽25), #14269163, #14269169, … |
| maximal normal subgroup of | D19×ΓL(1,𝔽25), #14269163, #14269169, … |
| maximal quotient of | C19×Dic3⋊C8, C19×#815, C19×(C2×D3)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 75);