Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C37 ⋊ C4 |
| Sylow | C37 ⋊ #444 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^31,d^b=df,g^b=g^36,g^c=g^31,g^e=g^3685 conjugacy classes — view the full character table.
| maximal subgroup of | #18011003, #18011004, #18011007, … |
| maximal normal subgroup of | #18011003, #18011004, #18011007, … |
| maximal quotient of | #18010186, #18010189, #18010194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1595);