Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#13063443 |
| derived, Sylow | C173 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10621924 |
| commutator, hypocenter | C173 | C82 |
| Frattini | C2×C4 | C2×#10621924 |
| Fitting | C2×C8×C173 | C4 |
| socle, prime radical | C22×C173 | C42 |
| cosocle | C4×Dic173 | C22 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C2×C8 | |
74 conjugacy classes of subgroups.
752 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#13063443, #36368474, #13063443⋊C16, … |
| maximal normal subgroup of | C16×#13063443, #36368474, #13063443⋊C16, … |
| maximal quotient of | #36368385, C16×#13063443, C8×#14583829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1389);