Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D11×#538 |
| Fitting | C11×#538 ⋊ C2 |
| Sylow | C11 ⋊ C2×#538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C11×#538 | C2 |
| hypercenter | #538 | D11 |
| hypocenter | C11 | C2×#538 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #538 | |
1336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1600, D11×#1606, D11×#1612, … |
| maximal normal subgroup of | D11×#1600, D11×#1606, D11×#1612, … |
| maximal quotient of | D11×#2312, D11×#2318, D11×#2321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17844);