Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #497 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^b=g^2381682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483853, #44483858, #44483863, … |
| maximal normal subgroup of | #44483853, #44483858, #44483863, … |
| maximal quotient of | #44484173, #44484180, #44484192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 941);