Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×#64470 |
| derived, Hall | C52⋊C3 ⋊ C4×C61 |
| Hall | C61×C52⋊C3 ⋊ C4 |
| Hall | C52×C61 ⋊ Dic3 |
| Sylow | C52 ⋊ Dic3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C61 | #3874 |
| commutator, hypocenter | C52⋊C3 | C4×C61 |
| Frattini | C2 | C61×#3874 |
| Fitting, socle | C2×C52×C61 | D3 |
| prime radical | C2×C61×C52⋊C3 | C2 |
| cosocle | C2×C52⋊C3 | C2×C61 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2×C61 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3660 |
1586 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 88);