Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C239 ⋊ #544 |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^238,c^b=ce2402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483487, #44483490, #44483521, … |
| maximal normal subgroup of | #44483487, #44483490, #44483521, … |
| maximal quotient of | #44487166, #44487172, #44487281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1180);