Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#6923 |
| Fitting | C8×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #6923 |
| commutator, hypocenter | C61 | C4×C8 |
| Frattini | C4 | C2×#6923 |
| Fitting | C8×C61 | C4 |
| socle | C2×C61 | C42 |
| prime radical | C2×D61 | C2×C4 |
| cosocle | C4×D61 | C22 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 488 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#6923, #16840649, C2×C8×#6923, … |
| maximal normal subgroup of | C16×#6923, #16840649, C2×C8×#6923, … |
| maximal quotient of | C8×#92420, #92420⋊C8, (C2×#6923)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 198);