Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C239 ⋊ C2 |
| Sylow | C239 ⋊ #518 |
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|a^2=f,b^a=be,d^a=de,c^b=ce,g^c=g^2382414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44484655, #44484827, #44484830, … |
| maximal normal subgroup of | #44484655, #44484827, #44484830, … |
| maximal quotient of | #44486900, #44486901, #44486903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1022);