Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20259370 |
| Fitting | C22×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D191 |
| commutator, cosocle | C2×C191 | C25 |
| Frattini | C2 | C24×D191 |
| Fitting | C22×Q8×C191 | C2 |
| socle | C22×C191 | C24 |
| hypercenter | C22×Q8 | D191 |
| hypocenter | C191 | C2×2−1+4 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
794 conjugacy classes of subgroups.
1934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37572478, #37572481, #37572492, … |
| maximal normal subgroup of | #37572478, #37572481, #37572492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1383);