Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43 |
No aliases for this group.
| Sylow | C71 ⋊ #13750 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D71 |
| commutator | C2×C71 | C2×C43 |
| Fitting | C2×#376×C71 | C2 |
| socle, prime radical, cosocle | C24×C71 | C24 |
| hypercenter | C2×#376 | D71 |
| hypocenter | C71 | #13750 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C2×#376 | |
2078 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 2078 conjugacy classes of subgroups — too many to draw. Only its 987 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=g,c^2=h,d^2=e,b^a=be,d^a=de,i^a=i^70,c^b=ce2936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 90654);