Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D541 |
| Fitting | C2×Q8×C541 ⋊ C2 |
| Sylow | C541 ⋊ C22×Q8 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D541, #103×D541, #46830182, … |
| maximal normal subgroup of | #101×D541, #103×D541, #46830182, … |
| maximal quotient of | C2×C4⋊C4×D541, C4×Q8×D541, C2×#31772593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 185);