Finite Group DatabasebetaFinite Group Databasebeta| order | 21536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C673 ⋊ C2 |
| Sylow | C673 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D673 |
| commutator, socle, cosocle | C22×C673 | C23 |
| Fitting | C24×C673 | C2 |
| hypercenter | C24 | D673 |
| hypocenter | C673 | #120 |
| LCS | G ▷ C22×C673 ▷ C673 | |
| UCS | C1 ◁ C22 ◁ C24 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5384 |
Polycyclic presentation:
2^5,673|b^a=bd,c^a=ce,f^a=f^6725390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21536, 115);