Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C113 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#90673 |
| commutator, socle | C2×C113 | C2×C8 |
| Fitting | C8×C113 | C4 |
| prime radical | C2×D113 | C8 |
| cosocle | #11744751 | C22 |
| hypercenter | C8 | #90673 |
| hypocenter | C113 | M32 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ C8 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1808 |
Polycyclic presentation:
2^5,113|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^98,f^b=f^112,f^c=f^112244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 221);