Finite Group DatabasebetaFinite Group Databasebeta| order | 4384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D4×C137 ⋊ C2 |
| Sylow | C137 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D137 |
| commutator, socle, cosocle | C22×C137 | C23 |
| Fitting | C2×D4×C137 | C2 |
| hypercenter | C2×D4 | D137 |
| hypocenter | C137 | #121 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^5,137|b^2=d,b^a=bd,c^a=ce,f^b=f^136694 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4384, 118);