Finite Group DatabasebetaFinite Group Databasebeta| order | 30592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #356×C239 ⋊ C2 |
| Sylow | C239 ⋊ #2133 |
230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^7,239|a^2=e,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=dg,e^b=efg,h^b=h^238,h^c=h^238,e^d=eg1570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30592, 6198);