Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D712 |
| Fitting | C23×C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D356 |
| commutator, cosocle | C4×C89 | C25 |
| Frattini | C4 | C24×D89 |
| Fitting | C23×C8×C89 | C2 |
| socle | C24×C89 | D4 |
| hypercenter | C23×C8 | D89 |
| hypocenter | C89 | C23×D8 |
| LCS | G ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
2872 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36461226, #36461228, #36461252, … |
| maximal normal subgroup of | #36461226, #36461228, #36461252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 19226);