Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C37 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C2×D37 |
| commutator | C2×C37 | C4×C8 |
| Fitting | C4×C8×C37 | C2 |
| socle, prime radical | C22×C37 | C42 |
| cosocle | C42×C37 | C22 |
| hypercenter | C4×C8 | D37 |
| hypocenter | C37 | #322 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^b=g^36616 conjugacy classes — view the full character table.
| maximal subgroup of | #17992516, #17992518, #17992571, … |
| maximal normal subgroup of | #17992516, #17992518, #17992571, … |
| maximal quotient of | #17992423, #17992514, #17992516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 270);