Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#20294100 |
| derived, Sylow | C433 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #13181884 |
| commutator, hypocenter | C433 | C22×C16 |
| Frattini | C4 | C22×#13181884 |
| Fitting | C22×C4×C433 | C4 |
| socle, prime radical | C23×C433 | C8 |
| cosocle | #16812358 | C23 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27712 |
1792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1602);