Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#20259257 |
| Sylow | C191 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37572398, #37572400, #37572403, … |
| maximal normal subgroup of | #37572398, #37572400, #37572403, … |
| maximal quotient of | C2×#27132413, C2×#27132415, #37571266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 594);