Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C67 ⋊ #2982 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D67 |
| commutator | C2×C67 | C23×C8 |
| Fitting | #431×C67 | C2 |
| socle | C22×C67 | C23×C4 |
| hypercenter | #431 | D67 |
| hypocenter | C67 | #2982 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^c=h^661388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30749696, #30749699, #30750478, … |
| maximal normal subgroup of | #30749696, #30749699, #30750478, … |
| maximal quotient of | #30854560, #30854561, #30854867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13590);