Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C37 ⋊ C4 |
| Sylow | C37 ⋊ #382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#3866 |
| commutator, socle | C22×C37 | C22×C4 |
| Fitting | C42×C37 | C4 |
| prime radical, cosocle | C22×D37 | C23 |
| hypercenter | C42 | #3866 |
| hypocenter | C37 | #382 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C42 | |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^a=g^31,g^f=g^36172 conjugacy classes — view the full character table.
| maximal subgroup of | #18009450, #18009451, #18009473, … |
| maximal normal subgroup of | #18009450, #18009451, #18009473, … |
| maximal quotient of | #18009772, #18009774, #18009782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1493);