Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#15667918 |
| derived, Sylow | C89 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D89 |
| commutator, hypocenter | C89 | C22×C32 |
| Frattini | C16 | C22×D89 |
| Fitting | C22×C16×C89 | C2 |
| socle, prime radical | C23×C89 | C16 |
| cosocle | C16×C89 | C23 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
2944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36442114, #36442115, #36442126, … |
| maximal normal subgroup of | #36442114, #36442115, #36442126, … |
| maximal quotient of | C2×C4×#15667918, C2×C22⋊#15667918, C2×C4⋊#15667918, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6799);