Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D67 |
| commutator, socle | C2×C67 | C22×C16 |
| Fitting | #504×C67 | C2 |
| hypercenter | #504 | D67 |
| hypocenter | C67 | #2258 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C16 ◁ #504 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^66,c^b=cg1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30776392, #30776395, #30776397, … |
| maximal normal subgroup of | #30776392, #30776395, #30776397, … |
| maximal quotient of | #30776011, #30776028, #30776317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6804);