Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C67 ⋊ #1422 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | D268 |
| commutator | C4×C67 | C2×C16 |
| Frattini | C2×C16 | C2×D67 |
| Fitting | C4×C16×C67 | C2 |
| socle | C2×C67 | C4⋊C16 |
| hypercenter | C4×C16 | D67 |
| hypocenter | C67 | #1422 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C16 ◁ C2×C16 ◁ C4×C16 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743275, #30743276, #30743278, … |
| maximal normal subgroup of | #30743275, #30743276, #30743278, … |
| maximal quotient of | #30743497, #30743504, #30743522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2708);