Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C13×#41 ⋊ C2 |
| Sylow | C13 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C23×D13 |
| commutator, socle, cosocle | C2×C13 | C25 |
| Frattini | C2 | C24×D13 |
| Fitting | C2×C13×#41 | C2 |
| hypercenter | C2×#41 | D13 |
| hypocenter | C13 | #585 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
810 conjugacy classes of subgroups; only the 443 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 443 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|c^2=f,e^a=ef,g^a=g^12,d^b=df154 conjugacy classes — view the full character table.
| maximal subgroup of | #13114785, #13114786, #13114798, … |
| maximal normal subgroup of | #13114785, #13114786, #13114798, … |
| maximal quotient of | #13128035, #13128037, #13128039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1614);