Finite Group DatabasebetaFinite Group Databasebeta| order | 24224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C757 ⋊ C2 |
| Sylow | C757 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D757 |
| commutator, socle, cosocle | C22×C757 | C23 |
| Fitting | C22⋊C4×C757 | C2 |
| hypercenter | C22⋊C4 | D757 |
| hypocenter | C757 | #121 |
| LCS | G ▷ C22×C757 ▷ C757 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12112 |
Polycyclic presentation:
2^5,757|b^2=d,b^a=bd,c^a=ce,f^b=f^756,f^c=f^7563794 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24224, 119);