Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C37 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D37 |
| commutator, socle | C2×C37 | C2×C16 |
| Fitting | C2×C16×C37 | C2 |
| prime radical | C22×C37 | C16 |
| cosocle | C16×C37 | C22 |
| hypercenter | C2×C16 | D37 |
| hypocenter | C37 | M64 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C16 ◁ C2×C16 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^36616 conjugacy classes — view the full character table.
| maximal subgroup of | #17992731, #17992732, #17992735, … |
| maximal normal subgroup of | #17992731, #17992732, #17992735, … |
| maximal quotient of | #17992730, C22⋊#11924442, C4⋊#11924442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 383);