Finite Group DatabasebetaFinite Group Databasebeta| order | 1888 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C59 ⋊ SD32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11745669 |
| commutator, cosocle | C8×C59 | C22 |
| Frattini | C8 | C2×D59 |
| Fitting, prime radical | D8×C59 | C2 |
| socle | C2×C59 | D8 |
| hypercenter | D8 | D59 |
| hypocenter | C59 | SD32 |
| LCS | G ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 944 |
Polycyclic presentation:
2^5,59|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^58,c^b=cd,d^b=de214 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D59, C2×#14273671, #16837831, … |
| maximal normal subgroup of | SD32×D59, C2×#14273671, #16837831, … |
| maximal quotient of | #16837203, #16837205, #16837229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1888, 90);