Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×C11⋊C16 |
| derived, Sylow | C11 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D11 |
| commutator, hypocenter | C11 | C22×C16 |
| Frattini | C8 | C22×D11 |
| Fitting | C22×C8×C11 | C2 |
| socle, prime radical | C23×C11 | C8 |
| cosocle | C8×C11 | C23 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #13066693, #13066694, #13066705, … |
| maximal normal subgroup of | #13066693, #13066694, #13066705, … |
| maximal quotient of | C2×C4×C11⋊C16, C2×C22⋊(C11⋊C16), C2×C4⋊(C11⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 628);