Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#120 ⋊ C2 |
| Sylow | C13 ⋊ B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #88191 |
| commutator, cosocle | C23×C13 | C23 |
| Frattini | C23 | C22×D13 |
| Fitting | C13×#120 | C2 |
| socle | C2×C13 | #120 |
| hypercenter | #120 | D13 |
| hypocenter | C13 | B(4,𝔽2) |
| LCS | G ▷ C23×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #120 | |
198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 198 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^a=cd,e^a=ef,g^a=g^12,c^b=ce,d^b=df100 conjugacy classes — view the full character table.
| maximal subgroup of | #13116820, #13116821, #13116826, … |
| maximal normal subgroup of | #13116820, #13116821, #13116826, … |
| maximal quotient of | #13113752, #13113753, #13113757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 659);