Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5×C11 |
| direct product | C3×#27130990 |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C4 |
| derived, Hall | C52×C112 ⋊ C3×C4 |
| Hall | C3×C112 ⋊ #1039 |
| Sylow | C112 ⋊ C3×#1039 |
| Hall | C3×C52 ⋊ #92150 |
| Sylow | C52 ⋊ C3×#92150 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #27130990 |
| commutator, hypocenter | C52×C112 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C112 | C4 |
| prime radical | C3×C52×C11⋊D11 | C2 |
| cosocle | C52×C11⋊D11 | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 ◁ C3 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
2334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 864);