Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C239 ⋊ C2 |
| Sylow | C239 ⋊ #396 |
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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=de,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^2382402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #396×D239, C2×#29504694, #44487784, … |
| maximal normal subgroup of | #396×D239, C2×#29504694, #44487784, … |
| maximal quotient of | #44482790, #44482792, #44482794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 471);