Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×#13083574 |
| Fitting | C2×C4×D4×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 | C2×C4×D4×C89 | C2 |
| hypercenter | C2×C4×D4 | D89 |
| hypocenter | C89 | D4×#41 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 | |
1648 conjugacy classes of subgroups.
1810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36446448, #36446452, #36521284, … |
| maximal normal subgroup of | #36446448, #36446452, #36521284, … |
| maximal quotient of | C22⋊C4×#13083574, C4⋊C4×#13083574, D4×#15667969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 17998);