Finite Group DatabasebetaFinite Group Databasebeta| order | 592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C37 ⋊ C2 |
| Sylow | C37 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D37 |
| commutator, socle, cosocle | C2×C37 | C23 |
| Frattini | C2 | C22×D37 |
| Fitting | C2×C4×C37 | C2 |
| hypercenter | C2×C4 | D37 |
| hypocenter | C37 | #41 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^4,37|b^2=d,c^a=cd,e^a=e^36154 conjugacy classes — view the full character table.
| maximal subgroup of | #11924462, #11924464, #11924542, … |
| maximal normal subgroup of | #11924462, #11924464, #11924542, … |
| maximal quotient of | #11924493, #11924495, C4×C22⋊D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(592, 38);