Finite Group DatabasebetaFinite Group Databasebeta| order | 4384 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C137 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #11764049 |
| commutator, hypocenter | C137 | C32 |
| Fitting | C4×C137 | C8 |
| socle, prime radical | C2×C137 | C16 |
| cosocle | #14555513 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^5,137|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^127,f^b=f^100,f^c=f^136100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4384, 236);