Finite Group DatabasebetaFinite Group Databasebeta| order | 30300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×C3⋊#1042 |
| unambiguous semidirect product | C3⋊(#1042×C101) |
| Fitting, socle, Hall | C3×C52×C101 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C4×C101 |
| Hall | C52×C101 ⋊ Dic3 |
| Hall | C3×C101 ⋊ #1042 |
| Sylow | C52 ⋊ Dic3×C101 |
| Sylow | C3 ⋊ #1042×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | C3⋊#1042 |
| commutator, hypocenter | C3×C52 | C4×C101 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C101 | C4 |
| prime radical | C3×C5×D5×C101 | C2 |
| cosocle | C3×C5×D5 | C2×C101 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C101 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6060 |
3333 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30300, 171);