Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C16 | C2×D67 |
| commutator | C2×C67 | C4×C16 |
| Fitting | C2×C32×C67 | C2 |
| socle | C22×C67 | C2×C16 |
| hypercenter | C2×C32 | D67 |
| hypocenter | C67 | #1397 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C16 ◁ C2×C32 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^662192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743637, #1397×D67, C2×#22558342, … |
| maximal normal subgroup of | #30743637, #1397×D67, C2×#22558342, … |
| maximal quotient of | #30743158, #30743163, #30743517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2643);