Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| isoclinism | isoclinic class of Dic122 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic122 |
| Sylow | C61 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D61 |
| commutator | C2×C61 | C22×C4 |
| Frattini | C22 | C22×D61 |
| Fitting | C42×C61 | C2 |
| socle, prime radical, cosocle | C22×C61 | C23 |
| hypercenter | C42 | D61 |
| hypocenter | C61 | C4×Q8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16839492, #16839494, C4×#11758200, … |
| maximal normal subgroup of | #16839492, #16839494, C4×#11758200, … |
| maximal quotient of | C4×C4⋊Dic61, C4×#11758196, #16839645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 112);