Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊Q8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #476 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=df,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^2381685 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483662, #44483663, #44483672, … |
| maximal normal subgroup of | #44483662, #44483663, #44483672, … |
| maximal quotient of | #44484545, #44484808, #44485130, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 836);