Finite Group DatabasebetaFinite Group Databasebeta| order | 752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D47 |
| commutator, socle, cosocle | C2×C47 | C23 |
| Fitting | Q8×C47 | C2 |
| hypercenter | Q8 | D47 |
| hypocenter | C47 | #41 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 376 |
Polycyclic presentation:
2^4,47|b^2=d,c^2=d,c^a=cd,e^a=e^46,c^b=cd125 conjugacy classes — view the full character table.
| maximal subgroup of | #13094045, #13094047, #13094051, … |
| maximal normal subgroup of | #13094045, #13094047, #13094051, … |
| maximal quotient of | #13093982, #13093986, Q8×Dic47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(752, 34);