Finite Group DatabasebetaFinite Group Databasebeta| order | 11216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic701 |
| derived, Sylow | C701 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D701 |
| commutator, hypocenter | C701 | C42 |
| Frattini | C22 | C2×D701 |
| Fitting | C2×C4×C701 | C2 |
| socle, prime radical, cosocle | C22×C701 | C22 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
2816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic701, #36376010, #36376026, … |
| maximal normal subgroup of | C8×Dic701, #36376010, #36376026, … |
| maximal quotient of | #36376007, C8×Dic701, C4×#19150480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11216, 16);