Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C433 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #16812367 |
| commutator, hypocenter | C433 | C4×C16 |
| Frattini | C4 | C2×#16812367 |
| Fitting | C8×C433 | C8 |
| socle | C2×C433 | C4×C8 |
| prime radical | C2×D433 | C2×C8 |
| cosocle | #20294105 | C22 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^6,433|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^354,g^b=g^254,g^c=g^179,g^d=g^432,g^e=g^432496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1642);