Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#14556050 |
| Fitting | C23×C8×C71 ⋊ C2 |
| Sylow | C71 ⋊ C22×#102 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D284 |
| commutator | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | C23×C8×C71 | C2 |
| socle | C24×C71 | D4 |
| hypercenter | C23×C8 | D71 |
| hypocenter | C71 | C22×#102 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31903015, #31903019, #31903713, … |
| maximal normal subgroup of | #31903015, #31903019, #31903713, … |
| maximal quotient of | C22×#17985728, C2×#22586766, C2×#22586740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 12997);