Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#19151508 |
| Fitting | C2×#95×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D89 |
| commutator, cosocle | C23×C89 | C24 |
| Frattini | C23 | C23×D89 |
| Fitting | C2×#95×C89 | C2 |
| socle | C24×C89 | C23 |
| hypercenter | C2×#95 | D89 |
| hypocenter | C89 | C2×#392 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36449436, #36449451, #36454623, … |
| maximal normal subgroup of | #36449436, #36449451, #36454623, … |
| maximal quotient of | C2×#26018492, C2×#26018498, C2×#26018517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7707);