Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C71 ⋊ #7556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C25 | C22×D71 |
| commutator | C23×C71 | C2×C42 |
| Fitting | C22×#95×C71 | C2 |
| socle, prime radical, cosocle | C25×C71 | C23 |
| hypercenter | C22×#95 | D71 |
| hypocenter | C71 | #7556 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C25 ◁ C22×#95 | |
2582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=h,c^2=d,b^a=bd,c^a=ce,c^b=cf,i^b=i^70,i^c=i^702888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 57493);