Finite Group DatabasebetaFinite Group Databasebeta| order | 26372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C19×D347 |
| unambiguous semidirect product | C347⋊(C22×C19) |
| unambiguous semidirect product | (C2×C347)⋊(C2×C19) |
| Fitting, socle | C2×C19×C347 ⋊ C2 |
| derived, Sylow | C347 ⋊ C22×C19 |
| Hall | C19×C347 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D347 |
| commutator, cosocle, hypocenter | C347 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C347 | C2 |
| LCS | G ▷ C347 | |
| UCS | C1 ◁ C2×C19 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13186 |
6650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26372, 7);