Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D113 |
| commutator, socle | C2×C113 | C22×C4 |
| Fitting, prime radical | #41×C113 | C2 |
| cosocle | C4×C113 | C23 |
| hypercenter | #41 | D113 |
| hypocenter | C113 | #131 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1808 |
Polycyclic presentation:
2^5,113|a^2=d,d^2=e,f^a=f^112,c^b=ce580 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 153);