Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×D4×C37 ⋊ C2 |
| Sylow | C37 ⋊ #392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D37 |
| commutator, socle, cosocle | C23×C37 | C23 |
| Fitting | C22×D4×C37 | C2 |
| hypercenter | C22×D4 | D37 |
| hypocenter | C37 | #392 |
| LCS | G ▷ C23×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
322 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 69 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^a=bd,c^a=ce,c^b=cf,g^c=g^36382 conjugacy classes — view the full character table.
| maximal subgroup of | #17993512, #17993517, #17993539, … |
| maximal normal subgroup of | #17993512, #17993517, #17993539, … |
| maximal quotient of | #17992835, #17992837, #17992838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 457);