Finite Group DatabasebetaFinite Group Databasebeta| order | 30675 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊(C409⋊C3) |
| unambiguous semidirect product | C409⋊(C52⋊C3) |
| Fitting, socle, derived, Hall | C52×C409 ⋊ C3 |
| Sylow | C409 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C409⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C409 | C3 |
| LCS | G ▷ C52×C409 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6135 |
Polycyclic presentation:
3,5^2,409|b^a=bc^4,c^a=b^3c^3,d^a=d^533411 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30675, 5);