Finite Group DatabasebetaFinite Group Databasebeta| order | 19698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#23754415 |
| Fitting, Hall | C2×C49×C67 ⋊ C3 |
| derived, Hall | C49×C67 ⋊ C2×C3 |
| Hall | C2×C67 ⋊ C49⋊C3 |
| Hall | C2×C49 ⋊ C67⋊C3 |
| Sylow | C67 ⋊ C2×C49⋊C3 |
| Sylow | C49 ⋊ C2×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #23754415 |
| commutator, cosocle, hypocenter | C49×C67 | C2×C3 |
| Frattini | C7 | C2×#13064105 |
| Fitting | C2×C49×C67 | C3 |
| socle | C2×C7×C67 | ΓL(1,𝔽8) |
| LCS | G ▷ C49×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6566 |
2194 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19698, 4);