Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C37 ⋊ #544 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | C2×C4⋊C4×C37 | C2 |
| prime radical | C23×C37 | C23 |
| hypercenter | C2×C4⋊C4 | D37 |
| hypocenter | C37 | #544 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^36,c^b=ce382 conjugacy classes — view the full character table.
| maximal subgroup of | #17993535, #17993538, #17993569, … |
| maximal normal subgroup of | #17993535, #17993538, #17993569, … |
| maximal quotient of | #17997214, #17997220, #17997329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1180);