Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C37 ⋊ C2 |
| Sylow | C37 ⋊ #385 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D37 |
| commutator | C22×C37 | C22×C4 |
| Fitting | #95×C37 | C2 |
| socle, cosocle | C23×C37 | C23 |
| prime radical | C23×D37 | C22 |
| hypercenter | #95 | D37 |
| hypocenter | C37 | #385 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #95 | |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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|a^2=f,b^2=f,b^a=bd,c^a=ce,g^a=g^36,g^c=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #385×D37, C2×#14557407, #17997034, … |
| maximal normal subgroup of | #385×D37, C2×#14557407, #17997034, … |
| maximal quotient of | #17992817, #17992830, #17992831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 423);