Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #41×D356 |
| Fitting | C4×#41×C89 ⋊ C2 |
| Sylow | C89 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Frattini | C22 | C24×D89 |
| Fitting | C4×#41×C89 | C2 |
| hypercenter | C4×#41 | D89 |
| hypocenter | C89 | D4×#41 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1648 conjugacy classes of subgroups.
1810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36446449, #36446453, #36521285, … |
| maximal normal subgroup of | #36446449, #36446453, #36521285, … |
| maximal quotient of | #41×#13083551, #41×C4⋊Dic89, #117×D356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18001);