Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2298 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C22×C71 | C23×C4 |
| Frattini | C23 | C23×D71 |
| Fitting | C4×C4⋊C4×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C4×C4⋊C4 | D71 |
| hypocenter | C71 | #2298 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
524 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=g,b^2=g,c^2=e,d^2=f,b^a=be,c^a=cf,h^c=h^701456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31890944, #31890947, #31995677, … |
| maximal normal subgroup of | #31890944, #31890947, #31995677, … |
| maximal quotient of | #31918570, #31918581, #31918593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7003);