Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C13 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #261 |
| commutator, hypocenter | C13 | C4×C16 |
| Frattini | C2×C4 | C2×#261 |
| Fitting | C2×C8×C13 | C4 |
| socle, prime radical | C22×C13 | C2×C8 |
| cosocle | C2×#1055 | C22 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^6,13|a^2=c,b^2=de,c^2=e,e^2=f,g^a=g^8,g^c=g^12112 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#1057, #13129747, #1057⋊C16, … |
| maximal normal subgroup of | C16×#1057, #13129747, #1057⋊C16, … |
| maximal quotient of | C8×#6092, #13129751, #13129875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 223);