Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C37 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#3866 |
| commutator, socle | C2×C37 | C23×C4 |
| Fitting | #41×C37 | C4 |
| prime radical | #41×D37 | C2 |
| cosocle | Dic37 | C24 |
| hypercenter | #41 | #3866 |
| hypocenter | C37 | #568 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ #41 | |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=e,e^2=f,d^a=df,g^a=g^31,c^b=cf,g^d=g^36,g^e=g^36124 conjugacy classes — view the full character table.
| maximal subgroup of | #18010557, #18010558, #18010593, … |
| maximal normal subgroup of | #18010557, #18010558, #18010593, … |
| maximal quotient of | #18011161, #18011167, #18011168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1628);