Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C37 ⋊ C2 |
| Sylow | C37 ⋊ #576 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D148 |
| commutator, cosocle | C4×C37 | C24 |
| Frattini | C4 | C23×D37 |
| Fitting | #131×C37 | C2 |
| socle | C2×C37 | C22×D4 |
| hypercenter | #131 | D37 |
| hypocenter | C37 | #576 |
| LCS | G ▷ C4×C37 ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|e^2=f,b^a=be,e^a=ef,g^a=g^36,e^b=ef,g^b=g^36,d^c=df382 conjugacy classes — view the full character table.
| maximal subgroup of | #17996551, #17996555, #17996565, … |
| maximal normal subgroup of | #17996551, #17996555, #17996565, … |
| maximal quotient of | #18003123, #18003196, #18003430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1354);