Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | #336×D71 |
| Fitting | #336×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#336 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator | C2×C71 | C2×C4×C8 |
| Fitting | #336×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | #336 | D71 |
| hypocenter | C71 | C2×#336 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
528 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1270×D71, #1271×D71, #1272×D71, … |
| maximal normal subgroup of | #1270×D71, #1271×D71, #1272×D71, … |
| maximal quotient of | #1273×D71, #31886832, #31886836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4199);