Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C4×#95×C83 ⋊ C2 |
| Sylow | C83 ⋊ #15141 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D83 |
| commutator, socle, cosocle | C24×C83 | C24 |
| Fitting | C4×#95×C83 | C2 |
| prime radical | C23×D332 | C22 |
| hypercenter | C4×#95 | D83 |
| hypocenter | C83 | #15141 |
| LCS | G ▷ C24×C83 ▷ C83 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
1906 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|a^2=ef,b^2=ef,c^2=e,d^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^82,c^b=cg3344 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 106271);