Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C239 ⋊ C2 |
| Sylow | C239 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^238,c^b=ce,g^b=g^2383836 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D239, C2×#29504501, #44482929, … |
| maximal normal subgroup of | D4⋊C8×D239, C2×#29504501, #44482929, … |
| maximal quotient of | #44482368, #44482370, #44482388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 278);