Finite Group DatabasebetaFinite Group Databasebeta| order | 2394 |
| isoclinism | isoclinic class of #14558802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C19 ⋊ C2×C9 |
| Hall | #11924781 ⋊ C2 |
| Hall | D133 ⋊ C9 |
| Sylow | C19 ⋊ D7⋊C9 |
| Sylow | C7 ⋊ AGL(1,𝔽19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C19 | C2×C9 |
| prime radical | (C19⋊C3)⋊D7 | C3 |
| cosocle | C7×C19⋊C3 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 133 |
Polycyclic presentation:
2,3^2,7,19|b^3=c,d^a=d^6,e^a=e^18,d^b=d^2,e^b=e^16,e^c=e^1128 conjugacy classes — view the full character table.
| maximal subgroup of | #14558802⋊C2, C2×#14558802, C5×#14558802, … |
| maximal normal subgroup of | #14558802⋊C2, C2×#14558802, C5×#14558802, … |
| maximal quotient of | #18012152, C2×#14558802, C5×#14558802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2394, 28);