Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C2×D67 |
| commutator, socle | C2×C67 | C22×C16 |
| Frattini | C16 | C22×D67 |
| Fitting | C2×C32×C67 | C2 |
| hypercenter | C2×C32 | D67 |
| hypocenter | C67 | #2258 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C32 ◁ C2×C32 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,d^2=e,e^2=f,f^2=g,c^b=cg,h^c=h^662192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743643, #30743645, #30776393, … |
| maximal normal subgroup of | #30743643, #30743645, #30776393, … |
| maximal quotient of | #30776009, #30776010, #30776026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6803);