Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #340×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1736 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D67 |
| commutator | C4×C67 | C2×C42 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #340×C67 | C2 |
| socle | C23×C67 | C2×D4 |
| hypercenter | #340 | D67 |
| hypocenter | C67 | #1736 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
448 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=f,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^66968 conjugacy classes — view the full character table.
| maximal subgroup of | #1736×D67, C2×#22559927, #30853237, … |
| maximal normal subgroup of | #1736×D67, C2×#22559927, #30853237, … |
| maximal quotient of | #30745291, #30745301, #30745313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4228);