Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, prime radical, cosocle | C22×C13 | C24 |
| Fitting | C4×Q8×C13 | C2 |
| hypercenter | C4×Q8 | D13 |
| hypocenter | C13 | #557 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^6,13|a^2=e,b^2=f,c^2=f,d^2=ef,d^a=de,g^a=g^12,c^b=cf145 conjugacy classes — view the full character table.
| maximal subgroup of | #13127516, #13127522, #13127527, … |
| maximal normal subgroup of | #13127516, #13127522, #13127527, … |
| maximal quotient of | Q8×#6101, #13117754, #13117757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1240);