Finite Group DatabasebetaFinite Group Databasebeta| order | 15752 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C11×C179 |
| multiplicative | (ℤ/23631)ˣ, (ℤ/31508)ˣ, (ℤ/47262)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C11×C179 |
| socle, prime radical | C22×C11×C179 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
32 conjugacy classes of subgroups.
15752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×C11×C179, C42×C11×C179, C22×C4×C11×C179 |
| maximal normal subgroup of | C2×C8×C11×C179, C42×C11×C179, C22×C4×C11×C179 |
| maximal quotient of | C2×C8×C11×C179, C42×C11×C179, C22×C4×C11×C179 |
Past the SmallGroups library coverage — no SmallGroups id.