Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#14555660 |
| derived, Sylow | C277 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D277 |
| commutator, hypocenter | C277 | C82 |
| Frattini | C42 | C2×D277 |
| Fitting | C4×C8×C277 | C2 |
| socle, prime radical | C22×C277 | C42 |
| cosocle | C42×C277 | C22 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
4480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#14555660, #47981083, #47981086, … |
| maximal normal subgroup of | C16×#14555660, #47981083, #47981086, … |
| maximal quotient of | #47980994, C16×#14555660, C8×#17984538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 269);