Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived | C3×C5×C132 ⋊ C22×C3 |
| Hall | C3×C5×C13×C13⋊C3 ⋊ C22 |
| Hall | C3×C13×C13⋊C3 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×C3×D3 |
| Sylow | C132 ⋊ C3×D3×D5 |
| Sylow | C5 ⋊ D13×C3⋊(D13⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C132 | C22×C3 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1170 |
Polycyclic presentation:
2^2,3^2,5,13^2|e^a=e^4,f^a=f^12,d^b=d^2,f^b=f^12,g^b=g^12,g^c=g^3402 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 703);