Finite Group DatabasebetaFinite Group Databasebeta| order | 30592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C239 ⋊ #2090 |
176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 15296 |
Polycyclic presentation:
2^7,239|a^2=eg,b^2=d,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^238,c^b=cf,f^b=fg,e^c=eg,f^c=fg2644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30592, 6023);