Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#14524212 |
| Fitting, socle, Hall | C5×C192 ⋊ D3 |
| derived, Hall | C5×#11762246 ⋊ C2 |
| Hall | #11762246 ⋊ D5 |
| Sylow | C192 ⋊ D15 |
| Sylow | C5 ⋊ #14524212 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#11762246 | C2 |
| Fitting, socle | C5×C192 | D3 |
| LCS | G ▷ C5×#11762246 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,19^2|b^a=b^2,c^a=c^4,d^a=e,e^a=d,d^b=d^11,e^b=e^7336 conjugacy classes — view the full character table.
| maximal subgroup of | #14524212⋊D5, #36343198, D5×#14524212, … |
| maximal normal subgroup of | #14524212⋊D5, #36343198, D5×#14524212, … |
| maximal quotient of | #36343144, C2×C5⋊#14524212, C5⋊#20266588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 40);