Finite Group DatabasebetaFinite Group Databasebeta| order | 30955 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C41×C151 ⋊ C5 |
| Sylow | C151 ⋊ C41⋊C5 |
| Sylow | C41 ⋊ C151⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C151 | C5 |
| LCS | G ▷ C41×C151 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6191 |
Polycyclic presentation:
5,41,151|b^a=b^16,c^a=c^81243 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30955, 5);