Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | Q82×Dic71 |
| Sylow | C71 ⋊ C4×Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D71 |
| commutator | C22×C71 | C24×C4 |
| Fitting | C2×Q82×C71 | C2 |
| socle, prime radical, cosocle | C23×C71 | C25 |
| hypercenter | C2×Q82 | D71 |
| hypocenter | C71 | C4×Q82 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×Q82 | |
2324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 329574);