Finite Group DatabasebetaFinite Group Databasebeta| order | 13968 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 110592 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C9×C97 |
| multiplicative | (ℤ/22173)ˣ, (ℤ/26205)ˣ, (ℤ/27952)ˣ, (ℤ/29564)ˣ, (ℤ/34940)ˣ, (ℤ/42012)ˣ, (ℤ/44346)ˣ, (ℤ/52410)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C97 |
| socle, prime radical | C23×C3×C97 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
162 conjugacy classes of subgroups.
13968 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C8×C9×C97, C2×C42×C9×C97, C23×C4×C9×C97 |
| maximal normal subgroup of | C22×C8×C9×C97, C2×C42×C9×C97, C23×C4×C9×C97 |
| maximal quotient of | C22×C8×C9×C97, C2×C42×C9×C97, C23×C4×C9×C97 |
Past the SmallGroups library coverage — no SmallGroups id.