Finite Group DatabasebetaFinite Group Databasebeta| order | 15176 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C7×C271 |
| multiplicative | (ℤ/22767)ˣ, (ℤ/30356)ˣ, (ℤ/45534)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C7×C271 |
| socle, prime radical | C22×C7×C271 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
32 conjugacy classes of subgroups.
15176 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C42×C7×C271, C2×C7×C8×C271, C22×C4×C7×C271 |
| maximal normal subgroup of | C42×C7×C271, C2×C7×C8×C271, C22×C4×C7×C271 |
| maximal quotient of | C42×C7×C271, C2×C7×C8×C271, C22×C4×C7×C271 |
Past the SmallGroups library coverage — no SmallGroups id.