Finite Group DatabasebetaFinite Group Databasebeta| order | 31936 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #117×C499 ⋊ C2 |
| Sylow | C499 ⋊ #536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D499 |
| commutator, socle, cosocle | C22×C499 | C24 |
| Fitting | #117×C499 | C2 |
| prime radical | C2×#22547811 | C2 |
| hypercenter | #117 | D499 |
| hypocenter | C499 | #536 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ #117 | |
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 15968 |
Polycyclic presentation:
2^6,499|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^498,c^b=ce,g^c=g^4985002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31936, 1125);