Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D113 |
| commutator, socle, prime radical, cosocle | C22×C113 | C23 |
| Fitting | C42×C113 | C2 |
| hypercenter | C42 | D113 |
| hypocenter | C113 | #125 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C42 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3616 |
Polycyclic presentation:
2^5,113|a^2=d,b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^112910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 138);