Finite Group DatabasebetaFinite Group Databasebeta| order | 11216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D2804 |
| Fitting | C2×C4×C701 ⋊ C2 |
| Sylow | C701 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D701 |
| commutator, cosocle | C2×C701 | C23 |
| Frattini | C2 | C22×D701 |
| Fitting | C2×C4×C701 | C2 |
| socle | C22×C701 | C22 |
| hypercenter | C2×C4 | D701 |
| hypocenter | C701 | C2×D4 |
| LCS | G ▷ C2×C701 ▷ C701 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
2810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36376016, #36376020, #36376022, … |
| maximal normal subgroup of | #36376016, #36376020, #36376022, … |
| maximal quotient of | C2×#26014283, C2×C4⋊Dic701, C4×D2804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11216, 36);