Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #413×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3067 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14524016 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #413×C67 | C2 |
| socle | C2×C67 | C2×#121 |
| hypercenter | #413 | D67 |
| hypocenter | C67 | #3067 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #413 | |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^66,f^c=fg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #30862768, #30862769, #30862779, … |
| maximal normal subgroup of | #30862768, #30862769, #30862779, … |
| maximal quotient of | #30838072, #30838100, #30838140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14229);