Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C241 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16838784 |
| commutator, hypocenter | C241 | C2×C32 |
| Frattini | C2 | C2×#16838784 |
| Fitting | C4×C241 | C16 |
| socle | C2×C241 | C2×C16 |
| prime radical | C2×D241 | C16 |
| cosocle | #16838782 | C22 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^111,g^b=g^240,g^c=g^30,g^d=g^177,g^e=g^240124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1678);