Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #95×C191 ⋊ C2 |
| Sylow | C191 ⋊ #399 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D191 |
| commutator, socle, cosocle | C23×C191 | C23 |
| Fitting | #95×C191 | C2 |
| prime radical | C23×D191 | C22 |
| hypercenter | #95 | D191 |
| hypocenter | C191 | #399 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ #95 | |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=de,b^a=bd,c^a=ce,c^b=cf,g^b=g^190,g^c=g^1901922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571541, #37571546, #37571569, … |
| maximal normal subgroup of | #37571541, #37571546, #37571569, … |
| maximal quotient of | #37570766, #37570785, #37570787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 486);