Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | C22⋊(C7⋊(C112⋊C9)) |
| unambiguous semidirect product | C7⋊(C22⋊(C112⋊C9)) |
| unambiguous semidirect product | C112⋊(C22⋊(C7⋊C9)) |
| derived, Hall | C22×C7×C112 ⋊ C9 |
| Hall | C7×C112 ⋊ C22⋊C9 |
| Hall | C22×C112 ⋊ C7⋊C9 |
| Sylow | C112 ⋊ C22⋊(C7⋊C9) |
| Hall | C22×C7 ⋊ C112⋊C9 |
| Sylow | C7 ⋊ C22⋊(C112⋊C9) |
| Sylow | C22 ⋊ C7⋊(C112⋊C9) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C7⋊(C112⋊C3)) |
| commutator, hypocenter | C22×C7×C112 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C7×C112 | C3 |
| LCS | G ▷ C22×C7×C112 | |
| UCS | C1 ◁ C3 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
Polycyclic presentation:
3,2^2,7,11^2,3|a^3=g,b^a=c,c^a=bc,d^a=d^2,e^a=e^9f,f^a=e^8f3396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 200);