Finite Group DatabasebetaFinite Group Databasebeta| order | 24224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C757 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D757 |
| commutator | C2×C757 | C22×C4 |
| Fitting | C4⋊C4×C757 | C2 |
| socle, prime radical, cosocle | C22×C757 | C23 |
| hypercenter | C4⋊C4 | D757 |
| hypocenter | C757 | C4×Q8 |
| LCS | G ▷ C2×C757 ▷ C757 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24224 |
Polycyclic presentation:
2^5,757|a^2=e,b^2=d,c^2=de,b^a=bd,f^c=f^7563800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24224, 111);