Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#11924511 |
| Fitting | C2×C4⋊C4×C37 ⋊ C2 |
| Sylow | C37 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D37 |
| commutator, cosocle | C22×C37 | C24 |
| Frattini | C22 | C23×D37 |
| Fitting | C2×C4⋊C4×C37 | C2 |
| socle | C23×C37 | C23 |
| hypercenter | C2×C4⋊C4 | D37 |
| hypocenter | C37 | C2×#121 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17994912, #17994917, #17995023, … |
| maximal normal subgroup of | #17994912, #17994917, #17995023, … |
| maximal quotient of | C2×#14557390, C2×#14557411, C2×#14557425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1042);