Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D52 |
| Fitting | C4×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C4×Q8×C13 | C2 |
| prime radical | C2×D52 | C22 |
| hypercenter | C4×Q8 | D13 |
| hypocenter | C13 | D4×Q8 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
145 conjugacy classes — view the full character table.
| maximal subgroup of | #13113937, #13113941, #13113999, … |
| maximal normal subgroup of | #13113937, #13113941, #13113999, … |
| maximal quotient of | Q8×#6103, C4⋊C4×D52, Q8×C4⋊Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1246);