Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C71×#2765 ⋊ C2 |
| Sylow | C71 ⋊ #36792 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D71 |
| commutator, socle, cosocle | C23×C71 | C25 |
| Fitting | C71×#2765 | C2 |
| prime radical | C2×#14556098 | C22 |
| hypercenter | #2765 | D71 |
| hypocenter | C71 | #36792 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #2765 | |
1906 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=g,d^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^b=i^70,i^d=i^70,i^e=i^701172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 378394);