Finite Group DatabasebetaFinite Group Databasebeta| order | 36822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C19 |
| direct product | C17×#14524207 |
| Fitting, socle, Hall | C17×C192 ⋊ C2×C3 |
| derived, Sylow | C192 ⋊ C2×C3×C17 |
| Hall | C17×#11762246 ⋊ C2 |
| Hall | C17×C19⋊D19 ⋊ C3 |
| Hall | #11762246 ⋊ C2×C17 |
| Hall | C19⋊D19 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #14524207 |
| commutator, cosocle, hypocenter | C192 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C192 | C2×C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C17 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 969 |
1122 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36822, 21);