Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#10623494 |
| derived, Sylow | C89 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D89 |
| commutator, hypocenter | C89 | C22×C4×C8 |
| Frattini | C2×C4 | C23×D89 |
| Fitting | C22×C42×C89 | C2 |
| socle, prime radical | C24×C89 | C2×C4 |
| cosocle | C2×C4×C89 | C24 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C22×C42 | |
760 conjugacy classes of subgroups.
2944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#26018079, #36443809, #36443811, … |
| maximal normal subgroup of | C2×#26018079, #36443809, #36443811, … |
| maximal quotient of | C22×C8×#10623494, C22×#19151319, C2×M16×#10623494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 12911);