Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#15690288 |
| Fitting | C4×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C4×#41 |
310 conjugacy classes of subgroups.
1940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570901, #37570906, #37570953, … |
| maximal normal subgroup of | #37570901, #37570906, #37570953, … |
| maximal quotient of | C4×#20259280, C4×#20259284, C4×Q8×Dic191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1019);