Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|c^2=d,d^2=f,b^a=bf,c^a=ce,g^a=g^10188 conjugacy classes — view the full character table.
| maximal subgroup of | #13066541, #13068566, #13068581, … |
| maximal normal subgroup of | #13066541, #13068566, #13068581, … |
| maximal quotient of | #13066962, #13066967, #13066971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 642);