Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C71 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×D71 |
| commutator, socle | C2×C71 | C2×C32 |
| Fitting | C2×C32×C71 | C2 |
| hypercenter | C2×C32 | D71 |
| hypocenter | C71 | M128 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C32 ◁ C2×C32 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^702320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31885258, #31885259, #31885262, … |
| maximal normal subgroup of | #31885258, #31885259, #31885262, … |
| maximal quotient of | #31885257, C22⋊(C71⋊C64), C4⋊(C71⋊C64), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2721);