Finite Group DatabasebetaFinite Group Databasebeta| order | 4384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C137 ⋊ C2 |
| Sylow | C137 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D137 |
| commutator, socle | C2×C137 | C22×C4 |
| Fitting | M16×C137 | C2 |
| prime radical | #14555510 | C2 |
| cosocle | C4×C137 | C23 |
| hypercenter | M16 | D137 |
| hypocenter | C137 | #131 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^5,137|a^2=d,d^2=e,f^a=f^136,c^b=ce,f^c=f^136700 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4384, 154);