Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊Dic239 |
| Sylow | C239 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
3848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482770, #44482771, #44482785, … |
| maximal normal subgroup of | #44482770, #44482771, #44482785, … |
| maximal quotient of | C22×C239⋊#95, C2×C4×C22⋊Dic239, C2×#29504628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 997);