Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#22603716 |
| Fitting | C2×C8×C571 ⋊ C2 |
| Sylow | C571 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
4580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142047, C4×#22603716, #49142218, … |
| maximal normal subgroup of | #49142047, C4×#22603716, #49142218, … |
| maximal quotient of | C2×#32912604, C4×#22603716, C2×(C2×D571)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 150);