Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#92420 |
| derived, Sylow | C61 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #6923 |
| commutator, hypocenter | C61 | C4×C8 |
| Frattini | C22 | C2×#6923 |
| Fitting | C2×C4×C61 | C4 |
| socle, prime radical | C22×C61 | C2×C4 |
| cosocle | C2×Dic61 | C22 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#92420, #16840603, #92420⋊C8, … |
| maximal normal subgroup of | C8×#92420, #16840603, #92420⋊C8, … |
| maximal quotient of | C8×#92420, #16840603, #16840628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 199);