Finite Group DatabasebetaFinite Group Databasebeta| order | 10072 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C17×C37 (order 5032) · Inn(G) = C1 · Out(G) = C23×C17×C37 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10072 |
| abelian | C8×C1259 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C2×C1259 |
| socle, prime radical | C2×C1259 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
10072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C1259, C2×C8×C1259, M16×C1259, … |
| maximal normal subgroup of | C16×C1259, C2×C8×C1259, M16×C1259, … |
| maximal quotient of | C16×C1259, C2×C8×C1259, C3×C8×C1259 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10072, 1);