Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | D4×#41×C71 ⋊ C2 |
| Sylow | C71 ⋊ #62729 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D71 |
| commutator, socle, cosocle | C22×C71 | C26 |
| Frattini | C22 | C25×D71 |
| Fitting | D4×#41×C71 | C2 |
| hypercenter | D4×#41 | D71 |
| hypocenter | C71 | #62729 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ D4×#41 | |
7346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,c^b=cg,d^b=dh,i^d=i^701826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 1076872);