Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle | C3×C5×C132 ⋊ C2×D3 |
| derived, Hall | C3×C5×#92789 ⋊ C22 |
| Hall | C3×#92789 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×C3⋊D3 |
| Sylow | C132 ⋊ C2×C3⋊D15 |
| Sylow | C5 ⋊ #20258913 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×#92789 | C22 |
| Fitting, socle | C3×C5×C132 | C2×D3 |
| LCS | G ▷ C3×C5×#92789 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 390 |
Polycyclic presentation:
2^2,3^2,5,13^2|c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^9g^2,g^a=f^12g^4,f^b=f^12,g^b=g^12,f^c=f^3g^11,g^c=g^9276 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 657);