Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#11758199 |
| Fitting | C2×D4×C61 ⋊ C2 |
| Sylow | C61 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D61 |
| commutator, cosocle | C4×C61 | C23 |
| Frattini | C4 | C22×D61 |
| Fitting | C2×D4×C61 | C2 |
| socle | C22×C61 | D4 |
| hypercenter | C2×D4 | D61 |
| hypocenter | C61 | C2×D8 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
314 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16839842, C4×#11758199, #16839871, … |
| maximal normal subgroup of | #16839842, C4×#11758199, #16839871, … |
| maximal quotient of | C2×#14519697, C2×#14519698, C2×#14519710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 156);