Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 764411904 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4×C9 |
| abelian | C22×C4×C8×C92 |
| multiplicative | (ℤ/20805)ˣ, (ℤ/21608)ˣ, (ℤ/22192)ˣ, (ℤ/22496)ˣ, (ℤ/27740)ˣ, (ℤ/31536)ˣ, (ℤ/31968)ˣ, (ℤ/32412)ˣ, (ℤ/39420)ˣ, (ℤ/41610)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32×C4 | C24×C32 |
| socle, prime radical | C24×C32 | C2×C32×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8740 conjugacy classes of subgroups.
10368 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.