Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C37 ⋊ C2 |
| Sylow | C37 ⋊ #539 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | C2×C4⋊C4×C37 | C2 |
| prime radical | #11924510 | C2 |
| hypercenter | C2×C4⋊C4 | D37 |
| hypocenter | C37 | #539 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|b^2=f,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^36,c^b=ce382 conjugacy classes — view the full character table.
| maximal subgroup of | #17993523, #17993527, #17993557, … |
| maximal normal subgroup of | #17993523, #17993527, #17993557, … |
| maximal quotient of | #17997199, #17997230, #17997265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1146);