Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#19152341 |
| Fitting | C2×#120×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D89 |
| commutator, cosocle | C22×C89 | C25 |
| Frattini | C22 | C24×D89 |
| Fitting | C2×#120×C89 | C2 |
| socle | C23×C89 | C24 |
| hypercenter | C2×#120 | D89 |
| hypocenter | C89 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36470251, #36470252, C2×#26022251, … |
| maximal normal subgroup of | #36470251, #36470252, C2×#26022251, … |
| maximal quotient of | C2×#26023390, C2×#26023391, C2×#26023393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18631);