Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#23751061 |
| Fitting | C2×C8×C599 ⋊ C2 |
| Sylow | C599 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
4804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305671, C4×#23751061, #50305842, … |
| maximal normal subgroup of | #50305671, C4×#23751061, #50305842, … |
| maximal quotient of | C2×#34062625, C4×#23751061, C2×(C2×D599)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 150);