Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#22593269 |
| Fitting | C2×#390×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#2539 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D71 |
| commutator, cosocle | C23×C71 | C25 |
| Frattini | C23 | C24×D71 |
| Fitting | C2×#390×C71 | C2 |
| socle | C24×C71 | C24 |
| hypercenter | C2×#390 | D71 |
| hypocenter | C71 | C2×#2539 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C2×#390 | |
5726 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
2036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 339599);