Finite Group DatabasebetaFinite Group Databasebeta| order | 752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic47⋊C4 |
| Sylow | C47 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D47 |
| commutator | C2×C47 | C2×C4 |
| Fitting | C2×C4×C47 | C2 |
| socle, prime radical, cosocle | C22×C47 | C22 |
| hypercenter | C2×C4 | D47 |
| hypocenter | C47 | C4⋊C4 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
Polycyclic presentation:
2^4,47|a^2=d,b^2=c,b^a=bd,e^a=e^46194 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C4×D47, C2×Dic47⋊C4, #13093980, … |
| maximal normal subgroup of | C4⋊C4×D47, C2×Dic47⋊C4, #13093980, … |
| maximal quotient of | C47⋊#95, Dic47⋊C8, #13093955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(752, 11);