Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#123 ⋊ C2 |
| Sylow | C13 ⋊ #546 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C13×#123 | C2 |
| hypercenter | #123 | D13 |
| hypocenter | C13 | #546 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #123 | |
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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=e,c^a=cf,g^a=g^12,d^b=de,d^c=df109 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#546, C2×#11719359, #13128319, … |
| maximal normal subgroup of | D13×#546, C2×#11719359, #13128319, … |
| maximal quotient of | #13117654, #13117660, #13117678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1325);