Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #557×C67 ⋊ C2 |
| Sylow | C67 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | #557×C67 | C2 |
| hypercenter | #557 | D67 |
| hypocenter | C67 | Q8×#41 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1068 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^66,h^d=h^66,h^e=h^66875 conjugacy classes — view the full character table.
| maximal subgroup of | #30831810, #30831818, #30831825, … |
| maximal normal subgroup of | #30831810, #30831818, #30831825, … |
| maximal quotient of | C4⋊C4×#11761629, #31015148, #31015258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 18092);