Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×D1108 |
| Fitting | C4×D4×C277 ⋊ C2 |
| Sylow | C277 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Fitting | C4×D4×C277 | C2 |
| hypercenter | C4×D4 | D277 |
| hypocenter | C277 | D42 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4432 |
2785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982220, #47982223, #47982282, … |
| maximal normal subgroup of | #47982220, #47982223, #47982282, … |
| maximal quotient of | D4×#17984540, C22⋊C4×D1108, D4×C4⋊Dic277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1185);