Finite Group DatabasebetaFinite Group Databasebeta| order | 24492 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C32×C42×C13 (order 7488) · Inn(G) = C1 · Out(G) = C22×C32×C42×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C24492 |
| abelian | C3×C4×C13×C157 |
| multiplicative | (ℤ/24649)ˣ, (ℤ/49298)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C3×C13×C157 |
| socle, prime radical | C2×C3×C13×C157 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
24492 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic12246, D24492 |
| maximal subgroup of | Dic12246, D24492 |
| maximal normal subgroup of | Dic12246, D24492 |
| automorphism group of | C24649 |
| outer automorphism group of | C24649 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24492, 1);