Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #553×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3565 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | #553×C67 | C2 |
| hypercenter | #553 | D67 |
| hypocenter | C67 | #3565 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #553 | |
930 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,c^2=f,d^2=fg,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^66,c^b=cg,d^b=df,h^d=h^66863 conjugacy classes — view the full character table.
| maximal subgroup of | #31752631, #31752635, #31752678, … |
| maximal normal subgroup of | #31752631, #31752635, #31752678, … |
| maximal quotient of | #31018885, #31018976, #31019137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19156);