Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C32 · Schur multiplier (H2) = C8 |
| direct product | C32×C71⋊C8 |
| derived, Sylow | C71 ⋊ C8×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C32 | D71 |
| commutator, hypocenter | C71 | C8×C32 |
| Frattini | C4×C16 | C2×D71 |
| Fitting | C4×C32×C71 | C2 |
| socle, prime radical | C22×C71 | C4×C16 |
| cosocle | C4×C16×C71 | C22 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C4×C32 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
4736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 56893);