Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#104 ⋊ C2 |
| Sylow | C13 ⋊ #453 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #88136 |
| commutator, cosocle | C2×C4×C13 | C23 |
| Frattini | C2×C4 | C22×D13 |
| Fitting | C13×#104 | C2 |
| socle | C2×C13 | #120 |
| hypercenter | #104 | D13 |
| hypocenter | C13 | #453 |
| LCS | G ▷ C2×C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #104 | |
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2^6,13|c^2=d,e^2=f,c^a=cd,e^a=ef,g^a=g^12,c^b=ce,d^b=df,e^b=ef100 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#453, C2×#11718483, #13124187, … |
| maximal normal subgroup of | D13×#453, C2×#11718483, #13124187, … |
| maximal quotient of | #13113755, #13113760, #13113783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 449);