Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11924623 |
| Sylow | C37 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #18010353, #18010354, #18010371, … |
| maximal normal subgroup of | #18010353, #18010354, #18010371, … |
| maximal quotient of | C2×#14558497, C2×#14558498, C4×#11924623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1624);