Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #126×C337 ⋊ C2 |
| Sylow | C337 ⋊ #529 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D337 |
| commutator, socle, cosocle | C22×C337 | C24 |
| Fitting | #126×C337 | C2 |
| prime radical | #24924932 | C2 |
| hypercenter | #126 | D337 |
| hypocenter | C337 | #529 |
| LCS | G ▷ C22×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ #126 | |
234 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10784 |
Polycyclic presentation:
2^6,337|b^2=f,d^2=e,b^a=be,c^a=cf,g^b=g^336,g^c=g^336,g^d=g^3362380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1082);