Finite Group DatabasebetaFinite Group Databasebeta| order | 17749 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C4×C9×C17×C29 (order 17748) · Inn(G) = C1 · Out(G) = C4×C9×C17×C29 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C17749 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
2 conjugacy classes of subgroups.
17749 conjugacy classes. The character table is too large to display.
| derived subgroup of | D17749 |
| Fitting subgroup of | D17749 |
| socle of | D17749 |
| maximal subgroup of | D17749, C2×C17749 |
| maximal normal subgroup of | D17749, C2×C17749 |
| maximal quotient of | C2×C17749 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17749, 1);