Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C433 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #20294111 |
| commutator, hypocenter | C433 | C2×C32 |
| Frattini | C2 | C2×#20294111 |
| Fitting | C4×C433 | C16 |
| socle | C2×C433 | C2×C16 |
| prime radical | C2×D433 | C16 |
| cosocle | #20294109 | C22 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13856 |
Polycyclic presentation:
2^6,433|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^238,g^b=g^432,g^c=g^354,g^d=g^179,g^e=g^432172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1678);