Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C61 ⋊ C3×C4×C5 |
| derived, Sylow | C61 ⋊ C3×C4×C52 |
| Hall | C5×#6923⋊C5 ⋊ C3 |
| Hall | C5×(C61⋊C3)⋊C5 ⋊ C4 |
| Hall | C5×C61⋊C5 ⋊ C3×C4 |
| Hall | #6923⋊C3 ⋊ C52 |
| Hall | #6923 ⋊ C3×C52 |
| Hall | C61⋊C3 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | AGL(1,𝔽61) |
| commutator, hypocenter | C61 | C3×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C61 | C3×C4×C5 |
| prime radical | C5×(D61⋊C3)⋊C5 | C2 |
| cosocle | D61 | C2×C3×C52 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 305 |
305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 112);