Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #405×C67 ⋊ C2 |
| Sylow | C67 ⋊ C4×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D67 |
| commutator | C2×C67 | C22×C42 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #405×C67 | C2 |
| socle | C22×C67 | C23×C4 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | C4×#131 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ #405 | |
572 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=f,e^2=g,h^b=h^66,d^c=dg,h^d=h^661400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30770878, #30770883, #30771767, … |
| maximal normal subgroup of | #30770878, #30770883, #30771767, … |
| maximal quotient of | #30821418, C8×#14524051, #30821442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12932);