Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C83 ⋊ #34584 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D83 |
| commutator, socle, cosocle | C23×C83 | C25 |
| Fitting | C83×#2618 | C2 |
| prime radical | C2×#121×C83 | C22 |
| hypercenter | #2618 | D83 |
| hypocenter | C83 | #34584 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #2618 | |
1774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dh,c^b=ch,i^e=i^821376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 336255);