Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8388608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C42×C8 |
| abelian | C3×C4×C8×C64 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C32 | C23×C3 |
| socle, prime radical | C23×C3 | C2×C4×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1776 conjugacy classes of subgroups.
6144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C4×C8×C128, C3×C4×C16×C64, C3×C82×C64, … |
| maximal normal subgroup of | C3×C4×C8×C128, C3×C4×C16×C64, C3×C82×C64, … |
| maximal quotient of | C3×C4×C8×C128, C3×C4×C16×C64, C3×C82×C64, … |
Past the SmallGroups library coverage — no SmallGroups id.