Finite Group DatabasebetaFinite Group Databasebeta| order | 4688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#11924078 |
| Fitting | C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#11924078 |
| commutator, socle | C2×C293 | C2×C4 |
| Fitting | C4×C293 | C4 |
| prime radical, cosocle | C2×D293 | C22 |
| hypercenter | C4 | #11924078 |
| hypocenter | C293 | C4⋊C4 |
| LCS | G ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1172 |
Polycyclic presentation:
2^4,293|a^2=d,b^2=c,b^a=bc,e^a=e^138,e^d=e^292302 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4688, 46);