Finite Group DatabasebetaFinite Group Databasebeta| order | 15729 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C107 · Schur multiplier (H2) = C7 |
| direct product | C107×#3862 |
| Fitting, socle, Hall | C72×C107 ⋊ C3 |
| derived, Sylow | C72 ⋊ C3×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | #3862 |
| commutator, cosocle, hypocenter | C72 | C3×C107 |
| Frattini | C1 | G |
| Fitting, socle | C72×C107 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C107 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2247 |
2033 conjugacy classes. The character table is too large to display.
| derived subgroup of | C107⋊#64418 |
| maximal subgroup of | C107×#64418, C107⋊#64418, C107×#64422, … |
| maximal normal subgroup of | C107×#64418, C107⋊#64418, C107×#64422, … |
| maximal quotient of | C2×C107×#3862 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15729, 4);