Finite Group DatabasebetaFinite Group Databasebeta| order | 30175 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C17 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C17×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C52×C17 |
| Hall | C17×C71 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | C71⋊C5 |
| commutator, cosocle, hypocenter | C71 | C52×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C5×C17 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6035 |
1615 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30175, 4);