Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #127×C37 ⋊ C2 |
| Sylow | C37 ⋊ #540 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | #127×C37 | C2 |
| hypercenter | #127 | D37 |
| hypocenter | C37 | #540 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #127 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^36,g^c=g^36274 conjugacy classes — view the full character table.
| maximal subgroup of | #18004792, #18004794, #18004837, … |
| maximal normal subgroup of | #18004792, #18004794, #18004837, … |
| maximal quotient of | #17997204, #17997233, #17997292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1153);