Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C13×#120 ⋊ C2 |
| Sylow | C13 ⋊ H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C13×#120 | C2 |
| hypercenter | #120 | D13 |
| hypocenter | C13 | H(3,𝔽4) |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #120 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|c^a=cf,d^a=def,g^a=g^12,c^b=ce,d^b=df103 conjugacy classes — view the full character table.
| maximal subgroup of | #13116835, #13116838, D13×H(3,𝔽4), … |
| maximal normal subgroup of | #13116835, #13116838, D13×H(3,𝔽4), … |
| maximal quotient of | #13117974, #13117975, #13117977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1265);