Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×Q32 ⋊ C2 |
| Sylow | C13 ⋊ #508 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D13 |
| commutator, cosocle | C8×C13 | C23 |
| Frattini | C8 | C22×D13 |
| Fitting | C13×Q32 | C2 |
| socle | C2×C13 | C2×D8 |
| hypercenter | Q32 | D13 |
| hypocenter | C13 | #508 |
| LCS | G ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|b^2=f,c^2=f,d^2=ef,e^2=f,b^a=bf,c^a=cf,g^a=g^12,c^b=cd,d^b=de,e^b=ef,d^c=de,e^c=ef88 conjugacy classes — view the full character table.
| maximal subgroup of | #13117144, #13117146, #13117150, … |
| maximal normal subgroup of | #13117144, #13117146, #13117150, … |
| maximal quotient of | #13116542, #13116617, #13116682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 546);