Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#14556313 |
| unambiguous semidirect product | D577⋊(C4⋊C4) |
| Fitting | C2×C4×C577 ⋊ C4 |
| Sylow | C577 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
1172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148822, #49148823, #49148828, … |
| maximal normal subgroup of | #49148822, #49148823, #49148828, … |
| maximal quotient of | C2×(C2×#14556313)⋊C4, C4×C4⋊#14556313, #49148891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 224);