Finite Group DatabasebetaFinite Group Databasebeta| order | 28192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#16812931 |
| Fitting | Q8×C881 ⋊ C4 |
| Sylow | C881 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#16812931 |
| commutator, socle | C2×C881 | C22×C4 |
| Fitting | Q8×C881 | C4 |
| prime radical, cosocle | C2×D881 | C23 |
| hypercenter | Q8 | #16812931 |
| hypocenter | C881 | C4×Q8 |
| LCS | G ▷ C2×C881 ▷ C881 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7048 |
1120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28192, 227);