Finite Group DatabasebetaFinite Group Databasebeta| order | 1820 |
| isoclinism | isoclinic class of C7⋊#63120 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#63120 |
| Fitting, socle, derived, Hall | C5×C7×C13 ⋊ C4 |
| Hall | C7×C13 ⋊ AGL(1,𝔽5) |
| Hall | C5×C13 ⋊ Dic7 |
| Hall | C5×C7 ⋊ Dic13 |
| Sylow | C13 ⋊ C7⋊AGL(1,𝔽5) |
| Sylow | C7 ⋊ #63120 |
| Sylow | C5 ⋊ Dic91 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C13 | C4 |
| prime radical, cosocle | C7×D5×C13 | C2 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 455 |
Polycyclic presentation:
2^2,5,7,13|a^2=b,c^a=c^2,d^a=d^6,e^a=e^12,c^b=c^4185 conjugacy classes — view the full character table.
| maximal subgroup of | C49⋊#63120, C7×C7⋊#63120, C7⋊(C7⋊#63120), … |
| maximal normal subgroup of | C7×C7⋊#63120, C11×C7⋊#63120, C13×C7⋊#63120, … |
| maximal quotient of | C49⋊#63120, C7×C7⋊#63120, C7⋊(C7⋊#63120), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1820, 18);