Finite Group DatabasebetaFinite Group Databasebeta| order | 24753 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C4×C9×C37 (order 15984) · Inn(G) = C1 · Out(G) = C22×C3×C4×C9×C37 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C24753 |
| abelian | C3×C37×C223 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
24753 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C37×C223, C3×C37×D223, C3×D37×C223, … |
| maximal normal subgroup of | C2×C3×C37×C223, C3×C37×D223, C3×D37×C223, … |
| maximal quotient of | C2×C3×C37×C223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24753, 7);