Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D4×C37 ⋊ C2 |
| Sylow | C37 ⋊ #553 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | C4×D4×C37 | C2 |
| hypercenter | C4×D4 | D37 |
| hypocenter | C37 | #553 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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=ef,d^2=e,b^a=be,c^a=cf,g^a=g^36,d^b=de,g^c=g^36385 conjugacy classes — view the full character table.
| maximal subgroup of | #18006451, #18006453, #18006503, … |
| maximal normal subgroup of | #18006451, #18006453, #18006503, … |
| maximal quotient of | #17997469, #17997485, #17997528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1249);