Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C37 ⋊ #384 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D37 |
| commutator | C22×C37 | C22×C4 |
| Fitting | C2×C42×C37 | C2 |
| socle, prime radical, cosocle | C23×C37 | C23 |
| hypercenter | C2×C42 | D37 |
| hypocenter | C37 | #384 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=d,c^2=e,b^a=bd,c^a=ce,g^a=g^36604 conjugacy classes — view the full character table.
| maximal subgroup of | #17992480, #17994596, #17994597, … |
| maximal normal subgroup of | #17992480, #17994596, #17994597, … |
| maximal quotient of | #17992826, #17992861, #17994748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 419);