Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #117×C191 ⋊ C2 |
| Sylow | C191 ⋊ #540 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D191 |
| commutator, socle, cosocle | C22×C191 | C24 |
| Fitting | #117×C191 | C2 |
| hypercenter | #117 | D191 |
| hypocenter | C191 | #540 |
| LCS | G ▷ C22×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ #117 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^190,c^b=ce1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37582719, #37582721, #37582763, … |
| maximal normal subgroup of | #37582719, #37582721, #37582763, … |
| maximal quotient of | #37575129, #37575164, #37575213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1154);