Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C13×H(5,𝔽2) ⋊ C2 |
| Sylow | C13 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D13 |
| commutator, socle, cosocle | C2×C13 | C25 |
| Fitting | C13×H(5,𝔽2) | C2 |
| hypercenter | H(5,𝔽2) | D13 |
| hypocenter | C13 | #585 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|c^2=f,e^a=ef,g^a=g^12,d^b=df,e^c=ef136 conjugacy classes — view the full character table.
| maximal subgroup of | #13124181, #13124186, #13124204, … |
| maximal normal subgroup of | #13124181, #13124186, #13124204, … |
| maximal quotient of | #13128034, #13128036, #13128040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1616);