Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C83 ⋊ C4⋊C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D83 |
| commutator | C22×C83 | C22×C42 |
| Fitting | C83×C4⋊#95 | C2 |
| socle, prime radical, cosocle | C24×C83 | C24 |
| hypercenter | C4⋊#95 | D83 |
| hypocenter | C83 | C4⋊C42 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C24 ◁ C4⋊#95 | |
1838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21248 |
Polycyclic presentation:
2^8,83|a^2=g,b^2=h,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,i^d=i^822396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 91004);