Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C71×#3444 ⋊ C2 |
| Sylow | C71 ⋊ #62686 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C23×D71 |
| commutator, socle, cosocle | C22×C71 | C26 |
| Frattini | C22 | C25×D71 |
| Fitting | C71×#3444 | C2 |
| hypercenter | #3444 | D71 |
| hypocenter | C71 | #62686 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C42 ◁ #3444 | |
7226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|e^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dh,c^b=ch,i^d=i^702048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 1076427);