Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#21439917 |
| Fitting | C2×C42×C239 ⋊ C2 |
| Sylow | C239 ⋊ C2×#117 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
3848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482860, #44482880, #44484243, … |
| maximal normal subgroup of | #44482860, #44482880, #44484243, … |
| maximal quotient of | C2×#29504618, C2×C4×(C2×D239)⋊C4, C2×C4×Dic239⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1003);