Finite Group DatabasebetaFinite Group Databasebeta| order | 1596 |
| isoclinism | isoclinic class of #11716328 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C19 ⋊ C3×C4 |
| Hall | Dic133 ⋊ C3 |
| Hall | #87705 ⋊ C4 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ (C19⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #11716328 |
| commutator, hypocenter | C7×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C19 | C2×C3 |
| prime radical | C2×#87705 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 532 |
Polycyclic presentation:
2,3,2,7,19|a^2=c,d^a=d^6,e^a=e^18,d^b=d^2,e^b=e^1156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1596, 12);