Finite Group DatabasebetaFinite Group Databasebeta| order | 33554 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D883 |
| unambiguous semidirect product | C883⋊(C2×C19) |
| Fitting, socle, Hall | C19×C883 ⋊ C2 |
| derived, Sylow | C883 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D883 |
| commutator, cosocle, hypocenter | C883 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C883 | C2 |
| LCS | G ▷ C883 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16777 |
8417 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33554, 2);