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 ⋊ #391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D37 |
| commutator | C22×C37 | C22×C4 |
| Fitting | C22×Q8×C37 | C2 |
| socle, prime radical, cosocle | C23×C37 | C23 |
| hypercenter | C22×Q8 | D37 |
| hypocenter | C37 | #391 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^a=g^36,g^b=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #17992722, #17994555, #17994557, … |
| maximal normal subgroup of | #17992722, #17994555, #17994557, … |
| maximal quotient of | #17992825, #17992828, #17992849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 456);