Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | C3×C11⋊(C11⋊#1043) |
| unambiguous semidirect product | C11⋊(C3×C11⋊#1043) |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C4 |
| derived, Hall | C52×C112 ⋊ C3×C4 |
| Hall | C3×C112 ⋊ #1043 |
| Sylow | C112 ⋊ C3×#1043 |
| Hall | C3×C52 ⋊ C11⋊Dic11 |
| Sylow | C52 ⋊ C3×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊(C11⋊#1043) |
| commutator, hypocenter | C52×C112 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C112 | C4 |
| prime radical | C3×C112×C5⋊D5 | C2 |
| cosocle | C112×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 ◁ C3 | |
672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
2550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 872);