Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#13083549 |
| derived, Sylow | C89 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D89 |
| commutator, hypocenter | C89 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D89 |
| Fitting | C2×C4×C8×C89 | C2 |
| socle, prime radical | C23×C89 | C2×C8 |
| cosocle | C2×C8×C89 | C23 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2×C4×C8 | |
216 conjugacy classes of subgroups.
2944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36441255, #36441256, #36441267, … |
| maximal normal subgroup of | #36441255, #36441256, #36441267, … |
| maximal quotient of | C2×C8×#13083549, C2×#26018170, M16×#13083549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6097);