Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D113 |
| commutator, socle, prime radical, cosocle | C22×C113 | C23 |
| Fitting | C4⋊C4×C113 | C2 |
| hypercenter | C4⋊C4 | D113 |
| hypocenter | C113 | C4⋊Q8 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3616 |
Polycyclic presentation:
2^5,113|a^2=d,b^2=d,c^2=e,b^a=bd,c^a=ce,f^b=f^112574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 145);