Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#10596964 |
| Fitting | C22×D4×C37 ⋊ C2 |
| Sylow | C37 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D37 |
| commutator, cosocle | C2×C37 | C25 |
| Frattini | C2 | C24×D37 |
| Fitting | C22×D4×C37 | C2 |
| socle | C23×C37 | C23 |
| hypercenter | C22×D4 | D37 |
| hypocenter | C37 | C22×#41 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17994512, #17994521, #17994533, … |
| maximal normal subgroup of | #17994512, #17994521, #17994533, … |
| maximal quotient of | C22×#11924492, C22×#11924494, C22×#11924496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1375);