Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C64×C67 ⋊ C2 |
| Sylow | C67 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×D67 |
| commutator, socle | C2×C67 | C2×C32 |
| Fitting | C64×C67 | C2 |
| hypercenter | C64 | D67 |
| hypocenter | C67 | M128 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C32 ◁ C64 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^662192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M128×D67, C2×#22558419, #30776869, … |
| maximal normal subgroup of | M128×D67, C2×#22558419, #30776869, … |
| maximal quotient of | #30743635, (C2×D67)⋊C64, Dic67⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2720);