Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C239 ⋊ #557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D239 |
| commutator, socle, prime radical, cosocle | C22×C239 | C24 |
| Fitting | C4×Q8×C239 | C2 |
| hypercenter | C4×Q8 | D239 |
| hypocenter | C239 | #557 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15296 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^2382405 conjugacy classes. The character table is too large to display.
| maximal quotient of | Q8×Dic239⋊C4, #44487466, #44487469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1275);