Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C433 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #20294111 |
| commutator, hypocenter | C433 | C64 |
| Fitting | C4×C433 | C16 |
| socle, prime radical | C2×C433 | C32 |
| cosocle | #28357310 | C2 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C4 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27712 |
Polycyclic presentation:
2^6,433|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^238,g^b=g^354,g^c=g^179,g^d=g^432172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1673);