Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | (C2×#261)⋊Q8 |
| Fitting | C2×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#261 |
| commutator, socle | C22×C13 | C22×C4 |
| Fitting | C2×Q8×C13 | C4 |
| prime radical, cosocle | C22×D13 | C23 |
| hypercenter | C2×Q8 | #261 |
| hypocenter | C13 | #391 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
186 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|a^2=d,b^2=f,c^2=f,c^a=ce,g^a=g^8,c^b=cf,g^d=g^1258 conjugacy classes — view the full character table.
| maximal subgroup of | #13129932, #13130683, #13130792, … |
| maximal normal subgroup of | #13129932, #13130683, #13130792, … |
| maximal quotient of | #13130013, #13130015, #13130021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1127);