Finite Group DatabasebetaFinite Group Databasebeta| order | 30861 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
| unambiguous semidirect product | C127⋊H(5,𝔽3) |
| Fitting | C3×H(3,𝔽3)×C127 ⋊ C3 |
| Sylow | C127 ⋊ H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C33×C127⋊C3 |
| commutator, socle, cosocle | C3×C127 | C34 |
| Fitting | C3×H(3,𝔽3)×C127 | C3 |
| hypercenter | C3×H(3,𝔽3) | C127⋊C3 |
| hypocenter | C127 | H(5,𝔽3) |
| LCS | G ▷ C3×C127 ▷ C127 | |
| UCS | C1 ◁ C3 ◁ C3×H(3,𝔽3) | |
586 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3429 |
Polycyclic presentation:
3^5,127|b^a=be,d^a=de,c^b=ce,f^d=f^1071469 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30861, 304);