Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊Dic457 |
| Sylow | C457 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14624 |
3668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416539, #44416540, #44416545, … |
| maximal normal subgroup of | #44416539, #44416540, #44416545, … |
| maximal quotient of | C2×#28410459, C4×C4⋊Dic457, #44416637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 101);