Finite Group DatabasebetaFinite Group Databasebeta| order | 1632 |
| isoclinism | isoclinic class of D17×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C24 |
| direct product | D17×C22⋊A4 |
| unambiguous semidirect product | C17⋊(C2×C22⋊A4) |
| Fitting, socle, derived | C24×C17 ⋊ C2×C3 |
| Hall | C24×D17 ⋊ C3 |
| Sylow | C17 ⋊ C2×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C17 | C2×C3 |
| LCS | G ▷ C24×C17 | |
| UCS | C1 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 204 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊A4×#595, D17×#1020, #72242960 |
| maximal normal subgroup of | C22⋊A4×#595, D17×#1020, #72242960 |
| maximal quotient of | D17×#997 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1632, 1204);