Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C64 · Schur multiplier (H2) = C23 |
| direct product | C2×C64×D83 |
| Fitting | C2×C64×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C22×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C64 | D83 |
| commutator, hypocenter | C83 | C22×C64 |
| Frattini | C32 | C22×D83 |
| Fitting | C2×C64×C83 | C2 |
| socle | C22×C83 | C2×C32 |
| prime radical | C22×D83 | C32 |
| cosocle | C32×C83 | C23 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C2×C64 | |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10624 |
5504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 90601);