Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D277 |
| Fitting | C4×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
2800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D277, #47981560, #47981594, … |
| maximal normal subgroup of | Q8⋊C8×D277, #47981560, #47981594, … |
| maximal quotient of | C4×C4⋊C4×D277, C4×#22579845, C4×Q8×Dic277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1012);