Finite Group DatabasebetaFinite Group Databasebeta| order | 12002 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C353 · Schur multiplier (H2) = C1 |
| direct product | D17×C353 |
| unambiguous semidirect product | C17⋊(C2×C353) |
| Fitting, socle, Hall | C17×C353 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C353 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C353 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C353 |
| Frattini | C1 | G |
| Fitting, socle | C17×C353 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C353 | |
8 conjugacy classes of subgroups.
3530 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #595×C353, #37562107, D17×D353, … |
| maximal normal subgroup of | #595×C353, #37562107, D17×D353, … |
| maximal quotient of | Dic17×C353, C2×D17×C353, C3×D17×C353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12002, 1);