Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C71 ⋊ #36701 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D71 |
| commutator, socle, prime radical, cosocle | C23×C71 | C25 |
| Fitting | C71×#2845 | C2 |
| hypercenter | #2845 | D71 |
| hypocenter | C71 | #36701 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
1304 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 501 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=h,b^2=h,c^2=f,d^2=f,e^2=g,b^a=bf,c^a=cg,d^a=dh,i^a=i^70,c^b=ch,d^c=dfh,i^c=i^70,i^e=i^70962 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 376293);