Finite Group DatabasebetaFinite Group Databasebeta| order | 1888 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D59 |
| commutator | C2×C59 | C22×C4 |
| Fitting | C4⋊C4×C59 | C2 |
| socle, cosocle | C22×C59 | C23 |
| prime radical | C22×D59 | C22 |
| hypercenter | C4⋊C4 | D59 |
| hypocenter | C59 | #117 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 944 |
Polycyclic presentation:
2^5,59|a^2=e,c^2=d,b^a=bd,f^b=f^58,f^c=f^58310 conjugacy classes — view the full character table.
| maximal subgroup of | #16837395, #16837397, #16837405, … |
| maximal normal subgroup of | #16837395, #16837397, #16837405, … |
| maximal quotient of | #16837247, #16837249, C4⋊C4×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1888, 104);