Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D152⋊C3 |
| Fitting | C8×C19 ⋊ C2×C3 |
| Hall | D152 ⋊ C3 |
| Hall | C19⋊C3 ⋊ D8 |
| Sylow | C19 ⋊ C3×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊(D19⋊C3) |
| commutator, cosocle | C4×C19 | C22×C3 |
| Frattini | C4 | C2×D19⋊C3 |
| Fitting | C8×C19 | C2×C3 |
| socle | C2×C19 | C3×D4 |
| hypercenter | C8 | D19⋊C3 |
| hypocenter | C19 | C3×D8 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^2,3,2^2,19|b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^18,f^c=f^745 conjugacy classes — view the full character table.
| maximal subgroup of | #10597257⋊C3, D304⋊C3, #10597283⋊C3, … |
| maximal normal subgroup of | #10597257⋊C3, D304⋊C3, #10597283⋊C3, … |
| maximal quotient of | #10597257⋊C3, D304⋊C3, Dic152⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 10);