Finite Group DatabasebetaFinite Group Databasebeta| order | 30300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#23758804 |
| Fitting, socle, Hall | C3×C52×C101 ⋊ C4 |
| derived, Hall | C52×C101 ⋊ C3×C4 |
| Hall | C3×C101 ⋊ #1043 |
| Sylow | C101 ⋊ C3×#1043 |
| Hall | C3×C52 ⋊ #87938 |
| Sylow | C52 ⋊ C3×#87938 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #23758804 |
| commutator, hypocenter | C52×C101 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C101 | C4 |
| prime radical | C3×C5⋊D505 | C2 |
| cosocle | C5⋊D505 | C2×C3 |
| LCS | G ▷ C52×C101 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7575 |
1905 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30300, 154);