Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#14556313 |
| unambiguous semidirect product | D577⋊C42 |
| Fitting | C2×C4×C577 ⋊ C4 |
| derived, Sylow | C577 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148814, #49148819, #49148821, … |
| maximal normal subgroup of | #49148814, #49148819, #49148821, … |
| maximal quotient of | C42×#14556313, C2×(C2×#14556313)⋊C4, #49148885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 222);