Finite Group DatabasebetaFinite Group Databasebeta| order | 3708 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C103 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×C103 |
| unambiguous semidirect product | C22⋊(C32×C103) |
| unambiguous semidirect product | (C22×C3)⋊(C3×C103) |
| Fitting, socle | C22×C3×C103 ⋊ C3 |
| derived, Sylow | C22 ⋊ C32×C103 |
| Hall | C22×C103 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C103 | A4 |
| commutator, cosocle, hypocenter | C22 | C32×C103 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C103 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C103 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1236 |
1236 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×A4×C103, C3×A5×C103, A4×ΓL(1,𝔽8)×C103, … |
| maximal normal subgroup of | C3×C5×A4×C103, C3×C7×A4×C103 |
| maximal quotient of | C3×C5×A4×C103, A4×ΓL(1,𝔽8)×C103, C3×C7×A4×C103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3708, 40);