Finite Group DatabasebetaFinite Group Databasebeta| order | 4384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C137 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#11764049 |
| commutator, socle | C2×C137 | C2×C8 |
| Fitting, prime radical | C22×C137 | C8 |
| cosocle | #11764047 | C22 |
| hypercenter | C22 | #11764049 |
| hypocenter | C137 | M32 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^5,137|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^127,f^c=f^100,f^d=f^13688 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4384, 242);