Finite Group DatabasebetaFinite Group Databasebeta| order | 19904 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4⋊Q8×C311 ⋊ C2 |
| Sylow | C311 ⋊ #556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D311 |
| commutator, socle, cosocle | C22×C311 | C24 |
| Fitting | C4⋊Q8×C311 | C2 |
| prime radical | C2×D1244 | C22 |
| hypercenter | C4⋊Q8 | D311 |
| hypocenter | C311 | #556 |
| LCS | G ▷ C22×C311 ▷ C311 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
212 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9952 |
Polycyclic presentation:
2^6,311|b^2=ef,c^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^310,d^b=de,g^b=g^310,g^c=g^3102195 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19904, 1273);