Finite Group DatabasebetaFinite Group Databasebeta| order | 20288 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C317 ⋊ C2 |
| Sylow | C317 ⋊ #556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D317 |
| commutator, socle, cosocle | C22×C317 | C24 |
| Fitting | C4×Q8×C317 | C2 |
| prime radical | C2×D1268 | C22 |
| hypercenter | C4×Q8 | D317 |
| hypocenter | C317 | #556 |
| LCS | G ▷ C22×C317 ▷ C317 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 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) = 10144 |
Polycyclic presentation:
2^6,317|b^2=ef,c^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^316,d^b=de,g^d=g^3163185 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20288, 1271);