Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#135 ⋊ C2 |
| Sylow | C13 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D13 |
| commutator, cosocle | C4×C13 | C24 |
| Frattini | C4 | C23×D13 |
| Fitting | C13×#135 | C2 |
| socle | C2×C13 | C22×D4 |
| hypercenter | #135 | D13 |
| hypocenter | C13 | #578 |
| LCS | G ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|c^2=f,d^2=f,e^2=f,b^a=bf,g^a=g^12,c^b=cf,d^b=df,d^c=de,e^c=ef,e^d=ef106 conjugacy classes — view the full character table.
| maximal subgroup of | #13116797, #13116801, #13116811, … |
| maximal normal subgroup of | #13116797, #13116801, #13116811, … |
| maximal quotient of | #13123365, #13123433, #13123672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1442);