Finite Group DatabasebetaFinite Group Databasebeta| order | 23776 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C743 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D743 |
| commutator | C2×C743 | C22×C4 |
| Fitting | C4⋊C4×C743 | C2 |
| socle, prime radical, cosocle | C22×C743 | C23 |
| hypercenter | C4⋊C4 | D743 |
| hypocenter | C743 | C4×Q8 |
| LCS | G ▷ C2×C743 ▷ C743 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23776 |
Polycyclic presentation:
2^5,743|a^2=e,b^2=d,c^2=de,b^a=bd,f^c=f^7423730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23776, 111);