Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C13×M16 ⋊ C4 |
| Sylow | C13 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#261 |
| commutator, socle | C2×C13 | C2×C42 |
| Fitting | C13×M16 | C4 |
| prime radical | C22×D13 | C2×C4 |
| cosocle | C4×D13 | C23 |
| hypercenter | M16 | #261 |
| hypocenter | C13 | #405 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ M16 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|a^2=d,c^2=e,d^2=f,e^2=f,g^a=g^8,c^b=cf,g^d=g^1270 conjugacy classes — view the full character table.
| maximal subgroup of | #13130593, #13130595, #13130612, … |
| maximal normal subgroup of | #13130593, #13130595, #13130612, … |
| maximal quotient of | M16×#1057, #13130034, #13130041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1065);