Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#11924532 |
| Fitting | C22×D4×C37 ⋊ C2 |
| Sylow | C37 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D37 |
| commutator, cosocle | C22×C37 | C24 |
| Frattini | C22 | C23×D37 |
| Fitting | C22×D4×C37 | C2 |
| socle | C23×C37 | C23 |
| hypercenter | C22×D4 | D37 |
| hypocenter | C37 | C2×#127 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17994991, #17994992, #17994994, … |
| maximal normal subgroup of | #17994991, #17994992, #17994994, … |
| maximal quotient of | C2×#14557402, C2×#14557433, C2×#14557434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1088);