Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2153 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D268 |
| commutator | C4×C67 | C22×C8 |
| Frattini | C2×C8 | C22×D67 |
| Fitting | #405×C67 | C2 |
| socle | C2×C67 | C2×C4⋊C8 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | #2153 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^66,c^b=cg1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30767348, #30767349, #30767353, … |
| maximal normal subgroup of | #30767348, #30767349, #30767353, … |
| maximal quotient of | #30767379, #30767405, #30767439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6276);