Finite Group DatabasebetaFinite Group Databasebeta| order | 11224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C3×C4×C5×C11 (order 5280) · Inn(G) = C1 · Out(G) = C23×C3×C4×C5×C11 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C11224 |
| abelian | C8×C23×C61 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C2×C23×C61 |
| socle, prime radical | C2×C23×C61 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
11224 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic11224, D22448 |
| maximal subgroup of | C16×C23×C61, C2×C8×C23×C61, D11224, … |
| maximal normal subgroup of | C16×C23×C61, C2×C8×C23×C61, D11224, … |
| maximal quotient of | C16×C23×C61, C2×C8×C23×C61 |
Past the SmallGroups library coverage — no SmallGroups id.