Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#16812367 |
| Fitting | C8×C433 ⋊ C8 |
| derived, Sylow | C433 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #16812367 |
| commutator, hypocenter | C433 | C82 |
| Frattini | C4 | C2×#16812367 |
| Fitting | C8×C433 | C8 |
| socle | C2×C433 | C4×C8 |
| prime radical | C2×D433 | C42 |
| cosocle | C4×#13181884 | C22 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3464 |
496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1632);