Finite Group DatabasebetaFinite Group Databasebeta| order | 32104 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C4013 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #30631065 |
| commutator, hypocenter | C4013 | C8 |
| Fitting, socle, prime radical | C2×C4013 | C4 |
| cosocle | Dic4013 | C2 |
| LCS | G ▷ C4013 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32104 |
Polycyclic presentation:
2^3,4013|a^2=b,b^2=c,d^a=d^1230,d^b=d^40122014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32104, 13);