Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C71 ⋊ Q8×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D71 |
| commutator | C22×C71 | C22×C42 |
| Fitting | C71×C4⋊#95 | C2 |
| socle, prime radical, cosocle | C24×C71 | C24 |
| hypercenter | C4⋊#95 | D71 |
| hypocenter | C71 | Q8×#95 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C4⋊#95 | |
2434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=h,c^2=f,d^2=fg,b^a=be,c^a=cf,d^b=de,i^d=i^702060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 91052);