Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C71×C128 ⋊ C2 |
| Sylow | C71 ⋊ M256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C64 | C2×D71 |
| commutator, socle | C2×C71 | C2×C64 |
| Fitting | C71×C128 | C2 |
| prime radical | C2×D71 | C64 |
| cosocle | C64×C71 | C22 |
| hypercenter | C128 | D71 |
| hypocenter | C71 | M256 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C64 ◁ C128 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bh,i^b=i^704640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 57478);