Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ #547 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C4×D4×C13 | C2 |
| hypercenter | C4×D4 | D13 |
| hypocenter | C13 | #547 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
292 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 115 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|b^2=f,d^2=e,c^a=cf,d^a=de,g^a=g^12,c^b=cf145 conjugacy classes — view the full character table.
| maximal subgroup of | #13113923, #13113927, #13113985, … |
| maximal normal subgroup of | #13113923, #13113927, #13113985, … |
| maximal quotient of | #13117661, #13117703, D4×C4⋊Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1226);