Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#20294109 |
| derived, Sylow | C433 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #16812367 |
| commutator, hypocenter | C433 | C22×C16 |
| Frattini | C2 | C22×#16812367 |
| Fitting, socle, prime radical | C23×C433 | C8 |
| cosocle | #16812365 | C23 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C23 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27712 |
496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1665);