Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 940032 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C17 |
| abelian | C4×C9×C172 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C2×C3×C172 |
| socle, prime radical | C2×C3×C172 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
180 conjugacy classes of subgroups.
10404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C9×C172, C2×C4×C9×C172, C4×C172×C27, … |
| maximal normal subgroup of | C8×C9×C172, C2×C4×C9×C172, C4×C172×C27, … |
| maximal quotient of | C8×C9×C172, C2×C4×C9×C172, C4×C172×C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 37);