Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C239 ⋊ C2 |
| Sylow | C239 ⋊ #385 |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=f,b^a=bd,c^a=ce,g^c=g^2382408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #385×D239, C2×#29504643, #44486985, … |
| maximal normal subgroup of | #385×D239, C2×#29504643, #44486985, … |
| maximal quotient of | #44482769, #44482779, #44482780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 420);