Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C37 ⋊ #398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D37 |
| commutator, socle, prime radical, cosocle | C23×C37 | C23 |
| Fitting | C2×C4⋊C4×C37 | C2 |
| hypercenter | C2×C4⋊C4 | D37 |
| hypocenter | C37 | #398 |
| LCS | G ▷ C23×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
150 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=e,b^2=d,c^2=d,b^a=bd,c^a=ce,g^a=g^36,c^b=cf382 conjugacy classes — view the full character table.
| maximal subgroup of | #398×D37, C2×#14557466, #17997838, … |
| maximal normal subgroup of | #398×D37, C2×#14557466, #17997838, … |
| maximal quotient of | #17992848, #17992849, #17992850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 482);