Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D571 |
| Fitting | C2×Q8×C571 ⋊ C2 |
| Sylow | C571 ⋊ C22×Q8 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
2870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D571, #103×D571, #49142273, … |
| maximal normal subgroup of | #101×D571, #103×D571, #49142273, … |
| maximal quotient of | C2×C4⋊C4×D571, C4×Q8×D571, C2×#32912659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 185);