Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#6090 |
| derived, Sylow | C13 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D13 |
| commutator, hypocenter | C13 | C22×C16 |
| Frattini | C8 | C22×D13 |
| Fitting | C22×C8×C13 | C2 |
| socle, prime radical | C23×C13 | C8 |
| cosocle | C8×C13 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #13112913, #13112914, #13112925, … |
| maximal normal subgroup of | #13112913, #13112914, #13112925, … |
| maximal quotient of | C2×C4×#6090, C2×C22⋊#6090, C2×C4⋊#6090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 723);