Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #489 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^238,c^b=cf,g^b=g^238,g^c=g^2381682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483852, #44483853, #44483862, … |
| maximal normal subgroup of | #44483852, #44483853, #44483862, … |
| maximal quotient of | #44484683, #44485237, #44485244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 911);