Finite Group DatabasebetaFinite Group Databasebeta| order | 37504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #542×C293 ⋊ C2 |
| Sylow | C293 ⋊ #3455 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D293 |
| commutator, socle, cosocle | C22×C293 | C25 |
| Fitting | #542×C293 | C2 |
| hypercenter | #542 | D293 |
| hypocenter | C293 | #3455 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #542 | |
1040 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^7,293|b^2=g,e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^292,h^d=h^292,h^e=h^2923256 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37504, 17897);