Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #405×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D71 |
| commutator | C2×C71 | C22×C42 |
| Fitting | #405×C71 | C2 |
| socle | C22×C71 | C23×C4 |
| hypercenter | #405 | D71 |
| hypocenter | C71 | #2875 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ #405 | |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^70,d^c=dg,h^d=h^701468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31912525, #31996030, #31996031, … |
| maximal normal subgroup of | #31912525, #31996030, #31996031, … |
| maximal quotient of | #31963044, #31963046, #31963063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 12937);