Finite Group DatabasebetaFinite Group Databasebeta| order | 10072 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C1259 · Schur multiplier (H2) = C1 |
| direct product | Q8×C1259 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C1259 | C22 |
| commutator, Frattini, cosocle | C2 | C22×C1259 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C1259 ◁ G | |
12 conjugacy classes of subgroups.
6295 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×C1259, Q16×C1259, C2×Q8×C1259, … |
| maximal normal subgroup of | SD16×C1259, Q16×C1259, C2×Q8×C1259, … |
| maximal quotient of | C4⋊C4×C1259, C2×Q8×C1259 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10072, 4);