Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×#121×C71 ⋊ C2 |
| Sylow | C71 ⋊ #36606 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D71 |
| commutator, socle, cosocle | C23×C71 | C25 |
| Fitting | C4×#121×C71 | C2 |
| prime radical | #22596683 | C2 |
| hypercenter | C4×#121 | D71 |
| hypocenter | C71 | #36606 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C4×#121 | |
2032 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=fh,b^2=fh,c^2=fh,d^2=gh,e^2=fh,b^a=bf,c^a=cg,c^b=ch,e^b=eh,i^b=i^70,d^c=dh,i^c=i^70,e^d=eh,i^d=i^70,i^e=i^702030 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 375355);