Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5×C11 |
| direct product | C22×C3×C5×#10597245 |
| Fitting, socle | C22×C3×C5×C112 ⋊ C5 |
| derived, Sylow | C112 ⋊ C22×C3×C52 |
| Hall | C22×C3×C112 ⋊ C52 |
| Hall | C22×C112 ⋊ C3×C52 |
| Hall | C3×C112 ⋊ C22×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C5 | #10597245 |
| commutator, cosocle, hypocenter | C112 | C22×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C5×C112 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C22×C3×C5 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3300 |
1740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 841);