Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic191 |
| derived, Sylow | C191 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D191 |
| commutator, hypocenter | C191 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D191 |
| Fitting | C22×C8×C191 | C2 |
| socle, prime radical | C23×C191 | C2×C4 |
| cosocle | C2×C4×C191 | C23 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
3104 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570597, #37570601, C4×C8×Dic191, … |
| maximal normal subgroup of | #37570597, #37570601, C4×C8×Dic191, … |
| maximal quotient of | C2×C8×C191⋊C8, C2×#27132385, C8×#15690271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 494);