Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | D21⋊(C3⋊(C11⋊D11)) |
| Fitting, socle, derived, Hall | C32×C7×C112 ⋊ C22 |
| Hall | C32×C112 ⋊ C2×D7 |
| Hall | C7×C112 ⋊ D32 |
| Sylow | C112 ⋊ (C3⋊D3)⋊D7 |
| Hall | C32×C7 ⋊ C2×C11⋊D11 |
| Sylow | C32 ⋊ D7×C11⋊D11 |
| Sylow | C7 ⋊ D3×C3⋊(C11⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C112 | C22 |
| LCS | G ▷ C32×C7×C112 | |
| UCS | C1 | |
616 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5082 |
Polycyclic presentation:
2^2,3^2,7,11^2|c^a=c^2,d^a=d^2,f^a=f^10,g^a=g^10,d^b=d^2,e^b=e^62187 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 451);