Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C37 ⋊ #376 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D37 |
| commutator | C2×C37 | C2×C42 |
| Fitting | #95×C37 | C2 |
| socle, prime radical, cosocle | C23×C37 | C23 |
| hypercenter | #95 | D37 |
| hypocenter | C37 | #376 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #95 | |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=e,b^2=f,c^2=d,b^a=bd,g^c=g^36400 conjugacy classes — view the full character table.
| maximal subgroup of | #17993079, #17993081, #17993102, … |
| maximal normal subgroup of | #17993079, #17993081, #17993102, … |
| maximal quotient of | #95×Dic37, #17992820, #17992822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 394);