Finite Group DatabasebetaFinite Group Databasebeta| order | 2604 |
| isoclinism | isoclinic class of #13049955 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C31 ⋊ C3×C4 |
| Hall | C7×Dic31 ⋊ C3 |
| Hall | #10620253 ⋊ C4 |
| Hall | Dic31 ⋊ ΓL(1,𝔽8) |
| Sylow | C31 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C31⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #13049955 |
| commutator, hypocenter | C7×C31 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C31 | C2×C3 |
| prime radical | C2×#10620253 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 868 |
Polycyclic presentation:
2,3,7,31,2|a^2=e,d^a=d^30,c^b=c^4,d^b=d^590 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14579596, #27189084, #14579596⋊C5, … |
| maximal normal subgroup of | C5×#14579596, #14579596⋊C5, C7×#14579596, … |
| maximal quotient of | C5×#14579596, #27189084, #27189153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2604, 7);