Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #456×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3020 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #120×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #456×C71 | C2 |
| socle | C2×C71 | C2×#120 |
| hypercenter | #456 | D71 |
| hypocenter | C71 | #3020 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #456 | |
698 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^70,e^b=eg,f^b=fg,e^c=eg,h^d=h^70589 conjugacy classes — view the full character table.
| maximal subgroup of | #32151635, #32151637, #32151641, … |
| maximal normal subgroup of | #32151635, #32151637, #32151641, … |
| maximal quotient of | #31969838, #31969872, #31969901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13875);