Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #127×C37 ⋊ C2 |
| Sylow | C37 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | #127×C37 | C2 |
| hypercenter | #127 | D37 |
| hypocenter | C37 | D42 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #127 | |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|b^a=be,c^a=cf,d^b=de,g^b=g^36,g^c=g^36,g^d=g^36277 conjugacy classes — view the full character table.
| maximal subgroup of | #17993648, #17993651, #17993710, … |
| maximal normal subgroup of | #17993648, #17993651, #17993710, … |
| maximal quotient of | #17997417, #17997496, #17997577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1184);