Finite Group DatabasebetaFinite Group Databasebeta| order | 37504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #529×C293 ⋊ C2 |
| Sylow | C293 ⋊ #3480 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C25 |
| Frattini | C22 | C24×D293 |
| Fitting | #529×C293 | C2 |
| hypercenter | #529 | D293 |
| hypocenter | C293 | #3480 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C2×C4 ◁ #529 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
Polycyclic presentation:
2^7,293|a^2=g,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^2924138 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37504, 18101);