Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C241 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #16838784 |
| commutator, hypocenter | C241 | C64 |
| Fitting | C4×C241 | C16 |
| socle, prime radical | C2×C241 | C32 |
| cosocle | #21440732 | C2 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C4 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15424 |
Polycyclic presentation:
2^6,241|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^111,g^b=g^30,g^c=g^177,g^d=g^240124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1673);