Finite Group DatabasebetaFinite Group Databasebeta| order | 28192 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#28381192 |
| derived, Sylow | C881 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #16812931 |
| commutator, hypocenter | C881 | C2×C16 |
| Frattini | C4 | C2×#16812931 |
| Fitting | C2×C4×C881 | C4 |
| socle, prime radical | C22×C881 | C8 |
| cosocle | #20296491 | C22 |
| LCS | G ▷ C881 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28192 |
1792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28192, 218);