Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #97×C37 ⋊ C2 |
| Sylow | C37 ⋊ #435 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D37 |
| commutator, socle | C22×C37 | C22×C4 |
| Fitting | #97×C37 | C2 |
| prime radical | C2×D148 | C4 |
| cosocle | C2×C4×C37 | C23 |
| hypercenter | #97 | D37 |
| hypocenter | C37 | #435 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^36,g^b=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #435×D37, C2×#14557606, #18003287, … |
| maximal normal subgroup of | #435×D37, C2×#14557606, #18003287, … |
| maximal quotient of | #17993427, #17993434, #17993441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 622);