Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#261 |
| commutator, socle | C2×C13 | C23×C4 |
| Fitting | C2×Q8×C13 | C4 |
| prime radical | C22×D13 | C23 |
| cosocle | C2×D13 | C24 |
| hypercenter | C2×Q8 | #261 |
| hypocenter | C13 | #519 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|a^2=e,b^2=f,c^2=f,d^a=df,g^a=g^8,c^b=cf,g^e=g^1264 conjugacy classes — view the full character table.
| maximal subgroup of | #13130792, #13130842, #13130844, … |
| maximal normal subgroup of | #13130792, #13130842, #13130844, … |
| maximal quotient of | #13131274, #13131276, #13131310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1593);