Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M64×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1400 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | (C2×D67)⋊C4 |
| commutator | C22×C67 | C2×C16 |
| Frattini | C2×C16 | C2×D67 |
| Fitting | M64×C67 | C2 |
| socle | C2×C67 | C22⋊C16 |
| hypercenter | M64 | D67 |
| hypocenter | C67 | #1400 |
| LCS | G ▷ C22×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C2×C16 ◁ M64 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^661364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1400×D67, C2×#22558348, #30776033, … |
| maximal normal subgroup of | #1400×D67, C2×#22558348, #30776033, … |
| maximal quotient of | #30743169, #30743229, #30743271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2649);