Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C67 ⋊ #2360 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | C4×C22⋊C4×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C4×C22⋊C4 | D67 |
| hypocenter | C67 | #2360 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
620 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,h^a=h^66,d^b=de,h^d=h^661370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2360×D67, C2×#22563215, #31015390, … |
| maximal normal subgroup of | #2360×D67, C2×#22563215, #31015390, … |
| maximal quotient of | C22⋊C4×Dic67⋊C4, #30777337, #30777340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7516);