Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#117×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D71 |
| commutator | C2×C71 | C24×C4 |
| Frattini | C22 | C24×D71 |
| Fitting | C2×#117×C71 | C2 |
| socle | C22×C71 | C25 |
| hypercenter | C2×#117 | D71 |
| hypocenter | C71 | #3428 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 | |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^c=h^701468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31902783, #31902786, #31902803, … |
| maximal normal subgroup of | #31902783, #31902786, #31902803, … |
| maximal quotient of | #32155664, #32155666, #32155678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17711);