Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C13 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×#261 |
| commutator, socle | C2×C13 | C2×C16 |
| Fitting | C2×C8×C13 | C4 |
| prime radical | C22×C13 | C16 |
| cosocle | #6090 | C22 |
| hypercenter | C2×C8 | #261 |
| hypocenter | C13 | M64 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^8,g^c=g^1288 conjugacy classes — view the full character table.
| maximal subgroup of | #13129947, #13129948, #13129951, … |
| maximal normal subgroup of | #13129947, #13129948, #13129951, … |
| maximal quotient of | #13129943, C22⋊#88036, C4⋊#88036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 215);