Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×#131 ⋊ C2 |
| Sylow | C13 ⋊ #472 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #88184 |
| commutator, cosocle | C2×C4×C13 | C23 |
| Frattini | C2×C4 | C22×D13 |
| Fitting | C13×#131 | C2 |
| socle | C2×C13 | #121 |
| hypercenter | #131 | D13 |
| hypocenter | C13 | #472 |
| LCS | G ▷ C2×C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #131 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|b^2=ef,d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,g^a=g^12,d^c=df136 conjugacy classes — view the full character table.
| maximal subgroup of | #13116793, #13116795, #13116800, … |
| maximal normal subgroup of | #13116793, #13116795, #13116800, … |
| maximal quotient of | #13114191, #13114196, #13114235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 769);