Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D523 |
| Fitting | C22×C4×C523 ⋊ C2 |
| Sylow | C523 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
4196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C22⋊D523)⋊C8, C8×C22⋊D523, #45690273, … |
| maximal normal subgroup of | (C22⋊D523)⋊C8, C8×C22⋊D523, #45690273, … |
| maximal quotient of | C4×C22⋊Dic523, C4×(C2×D523)⋊C4, C4×Dic523⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 107);