Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of C22⋊(C22⋊(C19⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C22⋊(C22⋊(C19⋊C3)) |
| unambiguous semidirect product | C19⋊(C22⋊A4) |
| Fitting, socle, derived, Hall | C24×C19 ⋊ C3 |
| Sylow | C19 ⋊ C22⋊A4 |
| Sylow | C24 ⋊ C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C19 | C3 |
| LCS | G ▷ C24×C19 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
Polycyclic presentation:
3,2^4,19|b^a=bc,c^a=b,d^a=de,e^a=d,f^a=f^7104 conjugacy classes — view the full character table.
| maximal subgroup of | #14269159, #120⋊(C19⋊C3), D19⋊(C22⋊A4), … |
| maximal normal subgroup of | #14269159, #120⋊(C19⋊C3), D19⋊(C22⋊A4), … |
| maximal quotient of | C22⋊(Q8⋊(C19⋊C3)), C19⋊#997, C2×C22⋊(C22⋊(C19⋊C3)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 218);