Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D61⋊C8 |
| unambiguous semidirect product | D61⋊(C2×C8) |
| derived, Sylow | C61 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #6923 |
| commutator, hypocenter | C61 | C22×C8 |
| Frattini | C2 | C22×#6923 |
| Fitting | C2×C4×C61 | C4 |
| socle | C22×C61 | C2×C4 |
| prime radical | C22×D61 | C4 |
| cosocle | Dic61 | C23 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#6923)⋊C8, #16840635, #16840637, … |
| maximal normal subgroup of | (C2×#6923)⋊C8, #16840635, #16840637, … |
| maximal quotient of | C2×C4×#92420, C4×D61⋊C8, D61⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 229);