Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C157 ⋊ C4 |
| Sylow | C157 ⋊ #157 |
| Sylow | C32 ⋊ #10597845 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C157 | C4 |
| LCS | G ▷ C32×C157 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,157|a^2=b,c^a=cd,d^a=cd^2,e^a=e^28,c^b=c^2,d^b=d^2,e^b=e^156357 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#19150810, #43246351, #43246352, … |
| maximal normal subgroup of | C5×#19150810 |
| maximal quotient of | C5×#19150810, #43246351, #43246352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 46);