Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #7554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C25 | C22×D71 |
| commutator | C22×C71 | C43 |
| Fitting | C23×C42×C71 | C2 |
| socle, prime radical, cosocle | C25×C71 | C23 |
| hypercenter | C23×C42 | D71 |
| hypocenter | C71 | #7554 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C25 ◁ C23×C42 | |
3158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=g,c^2=h,b^a=bd,c^a=ce,i^a=i^704592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 57488);