Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×C191⋊C8 |
| derived, Sylow | C191 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D191 |
| commutator, hypocenter | C191 | C23×C8 |
| Frattini | C4 | C23×D191 |
| Fitting | C23×C4×C191 | C2 |
| socle, prime radical | C24×C191 | C4 |
| cosocle | C4×C191 | C24 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C23×C4 | |
338 conjugacy classes of subgroups.
3104 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#27132417, C2×#27132418, #37572217, … |
| maximal normal subgroup of | C2×#27132417, C2×#27132418, #37572217, … |
| maximal quotient of | C22×C4×C191⋊C8, C22×C22⋊(C191⋊C8), C22×C4⋊(C191⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1306);