Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Q8×#11765849 |
| Sylow | C71 ⋊ Q8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Fitting | C2×C4×Q8×C71 | C2 |
| hypercenter | C2×C4×Q8 | D71 |
| hypocenter | C71 | Q8×M16 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
388 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31891785, #31891789, #31891799, … |
| maximal normal subgroup of | #31891785, #31891789, #31891799, … |
| maximal quotient of | C4⋊C4×#11765849, #31996104, Q8×#14556039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13464);