Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C8 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×C71⋊C8 |
| derived, Sylow | C71 ⋊ C2×C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D71 |
| commutator, hypocenter | C71 | C2×C42×C8 |
| Frattini | C22×C4 | C23×D71 |
| Fitting | C2×C43×C71 | C2 |
| socle, prime radical | C24×C71 | C22×C4 |
| cosocle | C22×C4×C71 | C24 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C43 | |
2046 conjugacy classes of subgroups; only the 1659 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1659 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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, 166888);