Finite Group DatabasebetaFinite Group Databasebeta| order | 5733 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C13 ⋊ C9 |
| Sylow | C72 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ #89204 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14274262 |
| commutator, hypocenter | C72×C13 | C9 |
| Fitting, socle | C3×C72×C13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
3,7^2,13,3|a^3=e,b^a=b^4,c^a=c^4,d^a=d^3645 conjugacy classes — view the full character table.
| maximal subgroup of | #26039445, #26039447, #26039455, … |
| maximal normal subgroup of | #26039445, #26039447, #26039455, … |
| maximal quotient of | C2×#19153199, C22⋊#19153199, C5×#19153199 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5733, 18);