Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D3×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D57⋊C4 |
| derived, Hall | C3×C19 ⋊ C22×C4 |
| Sylow | C19 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D19 |
| commutator, hypocenter | C3×C19 | C22×C4 |
| Frattini | C2 | C2×D3×D19 |
| Fitting, socle | C22×C3×C19 | C22 |
| prime radical | C22×D57 | C2 |
| cosocle | C2×C3×C19 | C23 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D57⋊C4, #14269300, #14269301, … |
| maximal normal subgroup of | C4×D57⋊C4, #14269300, #14269301, … |
| maximal quotient of | #14269202, #14269207, #14269213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 155);