Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C239⋊C64 |
| derived, Sylow | C239 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | D239 |
| commutator, hypocenter | C239 | C64 |
| Fitting, cosocle | C32×C239 | C2 |
| socle, prime radical | C2×C239 | C32 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C32 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15296 |
Polycyclic presentation:
2^6,239|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^2383872 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D239, C2×C239⋊C64, #44482758, … |
| maximal normal subgroup of | C64×D239, C2×C239⋊C64, #44482758, … |
| maximal quotient of | #44482367, C2×C239⋊C64 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 268);