Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C239 ⋊ C2 |
| Sylow | C239 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D239 |
| commutator, socle | C2×C239 | C22×C8 |
| Fitting | M32×C239 | C2 |
| prime radical | #16838548 | C4 |
| cosocle | C8×C239 | C23 |
| hypercenter | M32 | D239 |
| hypocenter | C239 | #504 |
| LCS | G ▷ C2×C239 ▷ C239 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=d,d^2=e,e^2=f,g^a=g^238,c^b=cf,g^c=g^2382420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486382, #44486384, #44486387, … |
| maximal normal subgroup of | #44486382, #44486384, #44486387, … |
| maximal quotient of | #44486146, #44486147, #44486160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 967);